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Journal articles on the topic 'Stochastic approximation techniques'

Author: Grafiati

Published: 15 February 2025

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1

Worden, Lee, Ira B. Schwartz, Simone Bianco, Sarah F. Ackley, Thomas M. Lietman, and Travis C. Porco. "Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics." Computational and Mathematical Methods in Medicine 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/4253167.

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We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.

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2

Bosch, Paul. "A Numerical Method for Two-Stage Stochastic Programs under Uncertainty." Mathematical Problems in Engineering 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/840137.

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Motivated by problems coming from planning and operational management in power generation companies, this work extends the traditional two-stage linear stochastic program by adding probabilistic constraints in the second stage. In this work we describe, under special assumptions, how the two-stage stochastic programs with mixed probabilities can be treated computationally. We obtain a convex conservative approximations of the chance constraints defined in second stage of our model and use Monte Carlo simulation techniques for approximating the expectation function in the first stage by the average. This approach raises with another question: how to solve the linear program with the convex conservative approximation (nonlinear constrains) for each scenario?

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3

Sengul, Suleyman, Zafer Bekiryazici, and Mehmet Merdan. "Wong-Zakai method for stochastic differential equations in engineering." Thermal Science 25, Spec. issue 1 (2021): 131–42. http://dx.doi.org/10.2298/tsci200528014s.

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In this paper, Wong-Zakai approximation methods are presented for some stochastic differential equations in engineering sciences. Wong-Zakai approximate solutions of the equations are analyzed and the numerical results are compared with results from popular approximation schemes for stochastic differential equations such as Euler-Maruyama and Milstein methods. Several differential equations from engineering problems containing stochastic noise are investigated as numerical examples. Results show that Wong-Zakai method is a reliable tool for studying stochastic differential equations and can be used as an alternative for the known approximation techniques for stochastic models.

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4

Capobianco, Enrico. "Computationally Efficient Atomic Representations for Nonstationary Stochastic Processes." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 03 (September 2003): 325–51. http://dx.doi.org/10.1142/s0219691303000177.

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Function approximation methods based on frames or other overcomplete dictionaries of approximating functions offer advantages over the orthogonal schemes due to the fact that the associated redundancy may lead to better de-noising and reconstruction power. Wavelet packets represent special wavelet frames; they combine overcompleteness with high time-frequency localization power through an optimal frequency-then-time segmentation. Compared to cosine packets, which enable optimal adaptation through time-then-frequency segmentation, wavelet packets show a different time-frequency resolution trade-off that might be useful for analyzing some kinds of non-stationary phenomena. We study the properties of covariance non-stationary stochastic processes whose realizations are observed at very high frequencies; the data are supplied by time series of a stock market return index. For these complex processes the effectiveness of wavelet and cosine packets is explored by implementing entropic optimization, greedy approximation techniques and dimension reduction methods.

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Najim, K., and E. Ikonen. "Distributed logic processors trained under constraints using stochastic approximation techniques." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 29, no. 4 (July 1999): 421–26. http://dx.doi.org/10.1109/3468.769763.

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6

Vande Wouwer, A., C. Renotte, and M. Remy. "Application of stochastic approximation techniques in neural modelling and control." International Journal of Systems Science 34, no. 14-15 (November 2003): 851–63. http://dx.doi.org/10.1080/00207720310001640296.

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7

Jaakkola, Tommi, Michael I. Jordan, and Satinder P. Singh. "On the Convergence of Stochastic Iterative Dynamic Programming Algorithms." Neural Computation 6, no. 6 (November 1994): 1185–201. http://dx.doi.org/10.1162/neco.1994.6.6.1185.

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Recent developments in the area of reinforcement learning have yielded a number of new algorithms for the prediction and control of Markovian environments. These algorithms, including the TD(λ) algorithm of Sutton (1988) and the Q-learning algorithm of Watkins (1989), can be motivated heuristically as approximations to dynamic programming (DP). In this paper we provide a rigorous proof of convergence of these DP-based learning algorithms by relating them to the powerful techniques of stochastic approximation theory via a new convergence theorem. The theorem establishes a general class of convergent algorithms to which both TD(λ) and Q-learning belong.

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8

Montes, Francisco, and Jorge Mateu. "On the MLE for a spatial point pattern." Advances in Applied Probability 28, no. 2 (June 1996): 339. http://dx.doi.org/10.1017/s0001867800048382.

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Parameter estimation for a two-dimensional point pattern is difficult because most of the available stochastic models have intractable likelihoods ([2]). An exception is the class of Gibbs or Markov point processes ([1], [5]), where the likelihood typically forms an exponential family and is given explicitly up to a normalising constant. However, the latter is not known analytically, so parameter estimates must be based on approximations ([3], [6], [7]). In this paper we present comparisons amongst the different techniques available in the literature to obtain an approximation of the maximum likelihood estimate (MLE). Two stochastic methods are specifically illustrated: a Newton-Raphson algorithm ([7]) and the Robbins-Monro procedure ([8]). We use a very simple point process model, the Strauss process ([4]), to test and compare those approximations.

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9

SUN, XU, XINGYE KAN, and JINQIAO DUAN. "APPROXIMATION OF INVARIANT FOLIATIONS FOR STOCHASTIC DYNAMICAL SYSTEMS." Stochastics and Dynamics 12, no. 01 (March 2012): 1150011. http://dx.doi.org/10.1142/s0219493712003614.

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Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random sets. Thus it is desirable to have some techniques to approximate random invariant foliations. In this paper, invariant foliations are approximated for dynamical systems with small noisy perturbations, via asymptotic analysis. Namely, random invariant foliations are represented as a perturbation of the deterministic invariant foliations, with deviation errors estimated.

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10

Schweiger, Regev, Eyal Fisher, Elior Rahmani, Liat Shenhav, Saharon Rosset, and Eran Halperin. "Using Stochastic Approximation Techniques to Efficiently Construct Confidence Intervals for Heritability." Journal of Computational Biology 25, no. 7 (July 2018): 794–808. http://dx.doi.org/10.1089/cmb.2018.0047.

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11

Chub, E. G., and V. A. Pogorelov. "Identification algorithm for telecommunication systems with uncertain parameters of their vector of state stochastic model." Journal of Physics: Conference Series 2131, no. 2 (December 1, 2021): 022090. http://dx.doi.org/10.1088/1742-6596/2131/2/022090.

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Abstract The described method of structure identification of the state vector of a telecommunication system stochastic model is based on a posteriori probability density approximation (APDA) by a system of a posteriori moments. An assumption of possible APDA approximation by a class of Pearson distributions resulted in a closed system of moment equations. Implementation of optimal non-linear stochastic object control techniques helped to solve the problem of structural identification. Introduction of the proposed approach into contemporary telecommunication systems will not impose additional requirements on the calculating equipment, thus making this method well-suited for a wide range of applications.

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12

BOUHADOU, S., and Y. OUKNINE. "STOCHASTIC EQUATIONS OF PROCESSES WITH JUMPS." Stochastics and Dynamics 14, no. 01 (December 29, 2013): 1350006. http://dx.doi.org/10.1142/s0219493713500068.

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We consider one-dimensional stochastic differential equations driven by white noises and Poisson random measure. We introduce new techniques based on local time prove new results on pathwise uniqueness and comparison theorems. Our approach is very easy to handle and do not need any approximation approach. Similar equations without jumps were studied in the same context by [8, 12] and other authors.

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13

Rihan, Fathalla A., Chinnathambi Rajivganthi, and Palanisamy Muthukumar. "Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control." Discrete Dynamics in Nature and Society 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/5394528.

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In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.

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Oladayo, ODUSELU-HASSAN, Emmanuel. "Advancing Hybrid Numerical Methods for Nonlinear Stochastic Differential Equations: Applications in Complex Systems." Asian Journal of Research in Computer Science 18, no. 1 (January 14, 2025): 124–32. https://doi.org/10.9734/ajrcos/2025/v18i1553.

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The focus of this work is to consider composite numerical techniques for the approximation of SDEs with nonlinear coefficients in the drift and diffusion terms. SDEs, crucial for modeling systems with stochastic components, contain nonlinear terms that cause analytical solvability, numerical stiffness, and sensitivity to noise. These difficulties pose a problem for traditional techniques such as Euler-Maruyama or Milstein schemes, specifically in stiff or very nonlinear systems. Accompanying exact methods are numerical methods that include a deterministic synthesis of drift terms and a stochastic interpolation of diffusion terms with the purpose of increasing precision and stability and optimizing used computing time. Discussed approaches include implicit-explicit (IMEX) schemes, spectral collocation methods, and machine learning-assisted techniques. IMEX methods handle stiffness in nonlinear drift terms implicitly, while explicitly handling stochastic diffusion. Spectral-collocation methods utilize high-order polynomial approximations for accuracy in discretization where solutions are smooth and defined in a bounded domain. The combination of these techniques and machine learning extends SDE analysis and concentrates on SDE nonlinearities as well as adaptive solution strategies. They find use in every area of discipline, such as stochastic volatility models in finance, population dynamics in biology, and turbulent fluid flows in engineering. Simulation results show that hybrid schemes outperform other methods in terms of accuracy, stability, and computational expense. This work outlines how the integration of the suggested methods can overcome the shortcomings of the classic approaches so as to enable progression in solving complex, high-dimensional, and nonlinear stochastic problems. Subsequent studies will continue to investigate additional adaptive frameworks and more domain-specific and machine learning-based improvements to expand the spectrum of hybrid use.

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15

Gacon, Julien, Christa Zoufal, Giuseppe Carleo, and Stefan Woerner. "Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information." Quantum 5 (October 20, 2021): 567. http://dx.doi.org/10.22331/q-2021-10-20-567.

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The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with d parameters, however, is computationally expensive and generally requires O(d2) function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines.

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16

Dhanalakshmi, K., and P. Balasubramaniam. "Exponential stability of second-order fractional stochastic integro-differential equations." Filomat 37, no. 9 (2023): 2699–715. http://dx.doi.org/10.2298/fil2309699d.

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In this paper studies the exponential stability result is derived for the second-order fractional stochastic integro-differential equations (FSIDEs) driven by sub-fractional Brownian motion (sub-fBm). By constructing a successive approximation method, we present pth moment exponential stability result of second-order FSIDEs using stochastic analysis techniques and fractional calculus (FC). At last, an example is demonstrated to illustrate the obtained theoretical result.

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17

Gani, J., and Sid Yakowitz. "Error bounds for deterministic approximations to Markov processes, with applications to epidemic models." Journal of Applied Probability 32, no. 4 (December 1995): 1063–76. http://dx.doi.org/10.2307/3215220.

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The computer age and the phenomenological complexity of the AIDS/HIV epidemic have engendered a rich profusion of deterministic and stochastic time series models for the development of an epidemic. The present study examines the reliability of deterministic approximations of fundamentally random processes. Through numerical analysis and probabilistic considerations, we derive absolute and simultaneous confidence interval bounding techniques, and offer a practical procedure based on these developments. A heartening aspect of the computational study presented at the close of this paper indicates that when the population size is in the thousands, the deterministic version to the classical logistic epidemic is a good approximation.

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18

Gani, J., and Sid Yakowitz. "Error bounds for deterministic approximations to Markov processes, with applications to epidemic models." Journal of Applied Probability 32, no. 04 (December 1995): 1063–76. http://dx.doi.org/10.1017/s0021900200103547.

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The computer age and the phenomenological complexity of the AIDS/HIV epidemic have engendered a rich profusion of deterministic and stochastic time series models for the development of an epidemic. The present study examines the reliability of deterministic approximations of fundamentally random processes. Through numerical analysis and probabilistic considerations, we derive absolute and simultaneous confidence interval bounding techniques, and offer a practical procedure based on these developments. A heartening aspect of the computational study presented at the close of this paper indicates that when the population size is in the thousands, the deterministic version to the classical logistic epidemic is a good approximation.

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19

Ojedokun, I. A., and F. O. Aweda. "Stochastic analysis of outage probability of the cascaded Rayleigh-Rician fading channel using Padé approximation method." Nigerian Journal of Technology 43, no. 2 (July 19, 2024): 208–16. http://dx.doi.org/10.4314/njt.v43i2.2.

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The dominance of wireless communication (WC) is evident in all areas of life such as Information and Communication Technology (ICT), research, business, academia, etc. However, modelling analysis of WC has been a serious challenge when it involves diversity combining. Previous work has attempted to solve this problem using approximation techniques. These approximation techniques seem to be complex and may be difficult to interpret. The existing practice of using the Probability Density Function (PDF) to analyse multipath fading in a diversity-rich environment is ineffective to handle cascaded fading channels. The current work proposed the Pade Approximation (PA) technique to mitigate the problem. The PA was developed from the generated Moment Generating Function (MGF) by truncating the Taylor series to obtain a rational expression. The approximated rational expressions obtained were transformed into PDF, Cumulative Density Function (CDF) and Outage Probability (Pout). The results show that the Pout reduces as the threshold value increases. The numerical results also shows that the diversity techniques is effective in combating fading because as the number of paths increases, the Pout reduces. The Pout reduces by 17.56% at L=4 from 90.83% at L=1 when there is no diversity. PA is a useful approximation to analyse the behavior of cascaded Rayleigh-Rician channel.

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20

Yan, Zuomao, and Fangxia Lu. "Complete Controllability of Fractional Impulsive Multivalued Stochastic Partial Integrodifferential Equations with State-Dependent Delay." International Journal of Nonlinear Sciences and Numerical Simulation 18, no. 3-4 (May 24, 2017): 197–220. http://dx.doi.org/10.1515/ijnsns-2016-0052.

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AbstractIn this article, we consider a class of fractional impulsive multivalued stochastic partial integrodifferential equations with state-dependent delay in a real separable Hilbert space. Sufficient conditions for the complete controllability of impulsive fractional stochastic evolution systems are established by means of the fixed-point theorem for discontinuous multivalued operators due to Dhage and properties of the $\alpha$-resolvent operator combined with approximation techniques. Two examples are also given to illustrate the obtained theorem.

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21

Mukherjee, Sayandev, and Terrence L. Fine. "Online Steepest Descent Yields Weights with Nonnormal Limiting Distribution." Neural Computation 8, no. 5 (July 1996): 1075–84. http://dx.doi.org/10.1162/neco.1996.8.5.1075.

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We study the asymptotic properties of the sequence of iterates of weight-vector estimates obtained by training a feedforward neural network with a basic gradient-descent method using a fixed learning rate and no batch-processing. Earlier results based on stochastic approximation techniques (Kuan and Hornik 1991; Finnoff 1993; Bucklew et al. 1993) have established the existence of a gaussian limiting distribution for the weights, but they apply only in the limiting case of a zero learning rate. We here prove, from an exact analysis of the one-dimensional case and constant learning rate, weak convergence to a distribution that is not gaussian in general. We also run simulations to compare and contrast the results of our analysis with those of stochastic approximation.

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22

Narayan, Akil, and Tao Zhou. "Stochastic Collocation on Unstructured Multivariate Meshes." Communications in Computational Physics 18, no. 1 (July 2015): 1–36. http://dx.doi.org/10.4208/cicp.020215.070515a.

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AbstractCollocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications. Selection of a collocation mesh is frequently a challenge, but methods that construct geometricallyunstructuredcollocation meshes have shown great potential due to attractive theoretical properties and direct, simple generation and implementation. We investigate properties of these meshes, presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.

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23

Yan, Zuomao. "On Approximate Controllability of Second-Order Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects." Journal of Function Spaces 2015 (2015): 1–26. http://dx.doi.org/10.1155/2015/925209.

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We discuss the approximate controllability of second-order impulsive neutral partial stochastic functional integrodifferential inclusions with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using the fixed point strategy, stochastic analysis, and properties of the cosine family of bounded linear operators combined with approximation techniques, a new set of sufficient conditions for approximate controllability of the second-order impulsive partial stochastic integrodifferential systems are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.

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24

Wu, F. C., and C. K. Wang. "Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model." Stochastic Hydrology and Hydraulics 12, no. 6 (December 15, 1998): 359–75. http://dx.doi.org/10.1007/s004770050025.

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25

Kovács, Mihály, Annika Lang, and Andreas Petersson. "Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 6 (November 2020): 2199–227. http://dx.doi.org/10.1051/m2an/2020012.

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The numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise is considered. A standard finite element method is employed for the spatial approximation and a a rational approximation of the exponential function for the temporal approximation. First, strong convergence of this approximation in both positive and negative order norms is proven. With the help of Malliavin calculus techniques this result is then used to deduce weak convergence rates for the class of twice continuously differentiable test functions with polynomially bounded derivatives. Under appropriate assumptions on the parameters of the equation, the weak rate is found to be essentially twice the strong rate. This extends earlier work by one of the authors to the semilinear setting. Numerical simulations illustrate the theoretical results.

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MOUHOUB, MALEK. "SYSTEMATIC VERSUS LOCAL SEARCH AND GA TECHNIQUES FOR INCREMENTAL SAT." International Journal of Computational Intelligence and Applications 07, no. 01 (March 2008): 77–96. http://dx.doi.org/10.1142/s1469026808002193.

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Propositional satisfiability (SAT) problem is fundamental to the theory of NP-completeness. Indeed, using the concept of "polynomial-time reducibility" all NP-complete problems can be polynomially reduced to SAT. Thus, any new technique for satisfiability problems will lead to general approaches for thousands of hard combinatorial problems. In this paper, we introduce the incremental propositional satisfiability problem that consists of maintaining the satisfiability of a propositional formula anytime a conjunction of new clauses is added. More precisely, the goal here is to check whether a solution to a SAT problem continues to be a solution anytime a new set of clauses is added and if not, whether the solution can be modified efficiently to satisfy the old formula and the new clauses. We will study the applicability of systematic and approximation methods for solving incremental SAT problems. The systematic method is based on the branch and bound technique, whereas the approximation methods rely on stochastic local search (SLS) and genetic algorithms (GAs). A comprehensive empirical study, conducted on a wide range of randomly generated consistent SAT instances, demonstrates the efficiency in time of the approximation methods over the branch and bound algorithm. However, these approximation methods do not guarantee the completeness of the solution returned. We show that a method we propose that uses nonsystematic search in a limited form together with branch and bound has the best compromise, in practice, between time and the success ratio (percentage of instances completely solved).

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Yuan, Jinlong, Jun Xie, Honglei Xu, Enmin Feng, and Zhilong Xiu. "Optimization for Nonlinear Uncertain Switched Stochastic Systems with Initial State Difference in Batch Culture Process." Complexity 2019 (February 3, 2019): 1–15. http://dx.doi.org/10.1155/2019/4979580.

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Based on the deterministic description of batch culture expressed in form of switched ordinary differential equations, we introduce a switched stochastic counterpart system with initial state difference together with uncertain switching instants and system parameters to model the process of glycerol biodissimilation to 1,3-propanediol (1,3-PD) induced byKlebsiella pneumoniae(K. pneumoniae). Important properties of the stochastic system are discussed. Our aim is to obtain the unified switched instants and system parameters under the condition of different initial states. To do this, we will formulate a system identification problem in which these uncertain switched instants and system parameters are regarded as decision variables to be chosen such that the relative error between experimental data and computational results is minimized. Such problem governed by the stochastic system is subject to continuous state inequality constraints and box constraints. By performing a time-scaling transformation as well as introducing the constraint transcription and local smoothing approximation techniques, we convert such problem into a sequence of approximation subproblems. Considering both the difficulty of finding analytical solutions and the complex nature of these subproblems, we develop a parallelized differential evolution (DE) algorithm to solve these approximation subproblems. From an extensive simulation, we show that the obtained optimal switched instants and system parameters are satisfactory with initial state difference.

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Tomberg, Eemeli. "Numerical stochastic inflation constrained by frozen noise." Journal of Cosmology and Astroparticle Physics 2023, no. 04 (April 1, 2023): 042. http://dx.doi.org/10.1088/1475-7516/2023/04/042.

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Abstract Stochastic inflation can resolve strong inflationary perturbations, which seed primordial black holes. I present a fast and accurate way to compute these perturbations in typical black hole producing single-field models, treating the short-wavelength Fourier modes beyond the de Sitter approximation. The squeezing and freezing of the modes reduces the problem to one dimension, and the resulting new form of the stochastic equations, dubbed `constrained stochastic inflation,' can be solved efficiently with semi-analytical techniques and numerical importance sampling. In an example case, the perturbation distribution is resolved in seconds deep into its non-Gaussian tail, a speed-up of factor 109 compared to a previous study. Along the way, I comment on the role of the momentum constraint in stochastic inflation.

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LIU, YONGCHAO, and GUI-HUA LIN. "CONVERGENCE ANALYSIS OF A REGULARIZED SAMPLE AVERAGE APPROXIMATION METHOD FOR STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS." Asia-Pacific Journal of Operational Research 28, no. 06 (December 2011): 755–71. http://dx.doi.org/10.1142/s0217595911003338.

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Regularization method proposed by Scholtes (2011) has been a recognized approach for deterministic mathematical programs with complementarity constraints (MPCC). Meng and Xu (2006) applied the approach coupled with Monte Carlo techniques to solve a class of one stage stochastic MPCC and presented some promising numerical results. However, Meng and Xu have not presented any convergence analysis of the regularized sample approximation method. In this paper, we fill out this gap. Specifically, we consider a general class of one stage stochastic mathematical programs with complementarity constraint where the objective and constraint functions are expected values of random functions. We carry out extensive convergence analysis of the regularized sample average approximation problems including the convergence of statistical estimators of optimal solutions, C-stationary points, M-stationary points and B-stationary points as sample size increases and the regularization parameter tends to zero.

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COSTANTINI, CRISTINA, and THOMAS G. KURTZ. "DIFFUSION APPROXIMATION FOR TRANSPORT PROCESSES WITH GENERAL REFLECTION BOUNDARY CONDITIONS." Mathematical Models and Methods in Applied Sciences 16, no. 05 (May 2006): 717–62. http://dx.doi.org/10.1142/s0218202506001339.

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Diffusion approximations are obtained for space inhomogeneous linear transport models with reflection boundary conditions. The collision kernel is not required to satisfy any balance condition and the scattering kernel on the boundary is general enough to include all examples of boundary conditions known to the authors (with conservation of the number of particles) and, in addition, to model the Debye sheath. The mathematical approach does not rely on Hilbert expansions, but rather on martingale and stochastic averaging techniques.

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Hu, Ying, Xiaomin Shi, and Zuo Quan Xu. "Constrained stochastic LQ control on infinite time horizon with regime switching." ESAIM: Control, Optimisation and Calculus of Variations 28 (2022): 5. http://dx.doi.org/10.1051/cocv/2021110.

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This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. To tackle the problem, two new extended stochastic Riccati equations (ESREs) on infinite time horizon are introduced. The existence of the nonnegative solutions, in both standard and singular cases, is proved through a sequence of ESREs on finite time horizon. Based on this result and some approximation techniques, we obtain the optimal state feedback control and optimal value for the stochastic LQ problem explicitly. Finally, we apply these results to solve a lifetime portfolio selection problem of tracking a given wealth level with regime switching and portfolio constraint.

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Ravikumar, K., K. Ramkumar, and Hamdy M. Ahmed. "Fractional neutral stochastic integrodifferential equations with Caputo fractional derivative: Rosenblatt process, Poisson jumps and Optimal control." Proyecciones (Antofagasta) 42, no. 3 (June 1, 2023): 549–70. http://dx.doi.org/10.22199/issn.0717-6279-4329.

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The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic integrodifferential equations driven by Rosenblatt process and Poisson jumps in Hilbert spaces. First we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using the successive approximation approach. The results are formulated and proved by using the fractional calculus, solution operator and stochastic analysis techniques. The existence of optimal control pairs of system governed by fractional neutral stochastic differential equations driven by Rosenblatt process and poisson jumps is also been presented. An example is provided to illustrate the theory.

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Randone, Francesca, Luca Bortolussi, and Mirco Tribastone. "Refining Mean-field Approximations by Dynamic State Truncation." ACM SIGMETRICS Performance Evaluation Review 49, no. 1 (June 22, 2022): 31–32. http://dx.doi.org/10.1145/3543516.3460099.

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Mean-field models are an established method to analyze large stochastic systems with N interacting objects by means of simple deterministic equations that are asymptotically correct when N tends to infinity. For finite N, mean-field equations provide an approximation whose accuracy is model- and parameter-dependent. Recent research has focused on refining the approximation by computing suitable quantities associated with expansions of order $1/N$ and $1/N^2$ to the mean-field equation. In this paper we present a new method for refining mean-field approximations. It couples the master equation governing the evolution of the probability distribution of a truncation of the original state space with a mean-field approximation of a time-inhomogeneous population process that dynamically shifts the truncation across the whole state space. We provide a result of asymptotic correctness in the limit when the truncation covers the state space; for finite truncations, the equations give a correction of the mean-field approximation. We apply our method to examples from the literature to show that, even with modest truncations, it is effective in models that cannot be refined using existing techniques due to non-differentiable drifts, and that it can outperform the state of the art in challenging models that cause instability due orbit cycles in their mean-field equations.

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Randone, Francesca, Luca Bortolussi, and Mirco Tribastone. "Refining Mean-field Approximations by Dynamic State Truncation." Proceedings of the ACM on Measurement and Analysis of Computing Systems 5, no. 2 (June 2021): 1–30. http://dx.doi.org/10.1145/3460092.

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Mean-field models are an established method to analyze large stochastic systems with N interacting objects by means of simple deterministic equations that are asymptotically correct when N tends to infinity. For finite N, mean-field equations provide an approximation whose accuracy is model- and parameter-dependent. Recent research has focused on refining the approximation by computing suitable quantities associated with expansions of order $1/N$ and $1/N^2$ to the mean-field equation. In this paper we present a new method for refining mean-field approximations. It couples the master equation governing the evolution of the probability distribution of a truncation of the original state space with a mean-field approximation of a time-inhomogeneous population process that dynamically shifts the truncation across the whole state space. We provide a result of asymptotic correctness in the limit when the truncation covers the state space; for finite truncations, the equations give a correction of the mean-field approximation. We apply our method to examples from the literature to show that, even with modest truncations, it is effective in models that cannot be refined using existing techniques due to non-differentiable drifts, and that it can outperform the state of the art in challenging models that cause instability due orbit cycles in their mean-field equations.

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Lee, Jinkyu. "Decomposition and Approximation Techniques for Large-scale Multistage Stochastic Programs: With Applications in Finance." Journal of the Korean Operations Research and Management Science Society 47, no. 1 (February 28, 2022): 15–42. http://dx.doi.org/10.7737/jkorms.2022.47.1.015.

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MAMONTOV, Y. V., and M. WILLANDER. "MODELLING OF HIGH-DIMENSIONAL DIFFUSION STOCHASTIC PROCESS WITH NONLINEAR COEFFICIENTS FOR ENGINEERING APPLICATIONS — PART II: APPROXIMATIONS FOR COVARIANCE AND SPECTRAL DENSITY OF STATIONARY PROCESS." Mathematical Models and Methods in Applied Sciences 09, no. 08 (November 1999): 1247–77. http://dx.doi.org/10.1142/s0218202599000555.

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This work is devoted to diffusion stochastic processes (DSPs) with nonlinear coefficients in n-dimensional Euclidean space at high n (n is much greater than a few units). It deals with covariance and spectral density of a stationary process whereas our accompanying work deals with expectation and variance of a nonstationary process. Combined, analytical–numerical approach is a reasonable and perhaps the only way to treat high-dimensional DSPs in practice. Each of the above works develops the corresponding parts of the analytical basis for this combined treatment. The present work proposes approximate analytical expressions for the covariance in the efficient integral form. The integral formula is based on the obtained analytical results for the covariance, allows for nonlinearities of the drift function, and is derived within DSP theory. No techniques directly related to stochastic differential equations are involved. The approximate expression for the covariance is also applied to evaluate the approximation for the spectral density. Some aspects of practical implementation of these approximations are discussed. The results of this work can equally be used in various engineering fields.

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Joshi, S., and R. Khardon. "Probabilistic Relational Planning with First Order Decision Diagrams." Journal of Artificial Intelligence Research 41 (June 21, 2011): 231–66. http://dx.doi.org/10.1613/jair.3205.

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Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on symbolic dynamic programming lifted these ideas to first order logic using several representation schemes. Recent work introduced a first order variant of decision diagrams (FODD) and developed a value iteration algorithm for this representation. This paper develops several improvements to the FODD algorithm that make the approach practical. These include, new reduction operators that decrease the size of the representation, several speedup techniques, and techniques for value approximation. Incorporating these, the paper presents a planning system, FODD-Planner, for solving relational stochastic planning problems. The system is evaluated on several domains, including problems from the recent international planning competition, and shows competitive performance with top ranking systems. This is the first demonstration of feasibility of this approach and it shows that abstraction through compact representation is a promising approach to stochastic planning.

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Waizmann, Tabea, Luca Bortolussi, Andrea Vandin, and Mirco Tribastone. "Improved estimations of stochastic chemical kinetics by finite-state expansion." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2251 (July 2021): 20200964. http://dx.doi.org/10.1098/rspa.2020.0964.

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Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

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Ding, Yonghong, and Yongxiang Li. "Approximate controllability of fractional stochastic evolution equations with nonlocal conditions." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 7-8 (November 18, 2020): 829–41. http://dx.doi.org/10.1515/ijnsns-2019-0229.

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AbstractThis paper deals with the approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We delete the compactness condition or Lipschitz condition for nonlocal term appearing in various literatures, and only need to suppose some weak growth condition on the nonlocal term. The discussion is based on the fixed point theorem, diagonal argument and approximation techniques. In the end, an example is presented to illustrate the abstract theory.

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Qimin, Zhang, and Li xining. "Existence and Uniqueness for Stochastic Age-Dependent Population with Fractional Brownian Motion." Mathematical Problems in Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/813535.

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A model for a class of age-dependent population dynamic system of fractional version with Hurst parameterh∈(1/2,1]is established. We prove the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients. The proofs of our results combine techniques of fractional Brownian motion calculus. Ideas of the finite-dimensional approximation by the Galerkin method are used.

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Venturi, D., and G. E. Karniadakis. "Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2166 (June 8, 2014): 20130754. http://dx.doi.org/10.1098/rspa.2013.0754.

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Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems.

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Zhang, E., R. Pintelon, and P. Guillaume. "Modal Identification Using OMA Techniques: Nonlinearity Effect." Shock and Vibration 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/178696.

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This paper is focused on an assessment of the state of the art of operational modal analysis (OMA) methodologies in estimating modal parameters from output responses of nonlinear structures. By means of the Volterra series, the nonlinear structure excited by random excitation is modeled as best linear approximation plus a term representing nonlinear distortions. As the nonlinear distortions are of stochastic nature and thus indistinguishable from the measurement noise, a protocol based on the use of the random phase multisine is proposed to reveal the accuracy and robustness of the linear OMA technique in the presence of the system nonlinearity. Several frequency- and time-domain based OMA techniques are examined for the modal identification of simulated and real nonlinear mechanical systems. Theoretical analyses are also provided to understand how the system nonlinearity degrades the performance of the OMA algorithms.

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LORIG, MATTHEW. "TIME-CHANGED FAST MEAN-REVERTING STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 14, no. 08 (December 2011): 1355–83. http://dx.doi.org/10.1142/s0219024911006875.

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We introduce a class of randomly time-changed fast mean-reverting stochastic volatility (TC-FMR-SV) models. Using spectral theory and singular perturbation techniques, we derive an approximation for the price of any European option in the TC-FMR-SV setting. Three examples of random time-changes are provided and are shown to induce distinct implied volatility surfaces. The key features of the TC-FMR-SV framework are that (i) it is able to incorporate jumps into the price process of the underlying asset (ii) it allows for the leverage effect and (iii) it can accommodate multiple factors of volatility, which operate on different time-scales.

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Macindoe, Owen. "Assistant Agents for Sequential Planning Problems." Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment 8, no. 6 (June 30, 2021): 27–30. http://dx.doi.org/10.1609/aiide.v8i6.12486.

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The problem of optimal planning under uncertainty in collaborative multi-agent domains is known to be deeply intractable but still demands a solution. This thesis will explore principled approximation methods that yield tractable approaches to planning for AI assistants, which allow them to understand the intentions of humans and help them achieve their goals. AI assistants are ubiquitous in video games, mak- ing them attractive domains for applying these planning techniques. However, games are also challenging domains, typically having very large state spaces and long planning horizons. The approaches in this thesis will leverage recent advances in Monte-Carlo search, approximation of stochastic dynamics by deterministic dynamics, and hierarchical action representation, to handle domains that are too complex for existing state of the art planners. These planning techniques will be demonstrated across a range of video game domains.

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Kompas, Tom, and Long Chu. "Comparing approximation techniques to continuous-time stochastic dynamic programming problems: Applications to natural resource modelling." Environmental Modelling & Software 38 (December 2012): 1–12. http://dx.doi.org/10.1016/j.envsoft.2012.04.002.

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Hauskrecht, M. "Value-Function Approximations for Partially Observable Markov Decision Processes." Journal of Artificial Intelligence Research 13 (August 1, 2000): 33–94. http://dx.doi.org/10.1613/jair.678.

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Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a set of imperfect or noisy observations. The modeling advantage of POMDPs, however, comes at a price -- exact methods for solving them are computationally very expensive and thus applicable in practice only to very simple problems. We focus on efficient approximation (heuristic) methods that attempt to alleviate the computational problem and trade off accuracy for speed. We have two objectives here. First, we survey various approximation methods, analyze their properties and relations and provide some new insights into their differences. Second, we present a number of new approximation methods and novel refinements of existing techniques. The theoretical results are supported by experiments on a problem from the agent navigation domain.

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Wang, Xuhui, Sheng-Jhih Wu, and Xingye Yue. "Pricing timer options: second-order multiscale stochastic volatility asymptotics." ANZIAM Journal 63 (October 2, 2021): 249–67. http://dx.doi.org/10.21914/anziamj.v63.15291.

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We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated. doi:10.1017/S1446181121000249

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BROADIE, MARK, and ASHISH JAIN. "THE EFFECT OF JUMPS AND DISCRETE SAMPLING ON VOLATILITY AND VARIANCE SWAPS." International Journal of Theoretical and Applied Finance 11, no. 08 (December 2008): 761–97. http://dx.doi.org/10.1142/s0219024908005032.

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We investigate the effect of discrete sampling and asset price jumps on fair variance and volatility swap strikes. Fair discrete volatility strikes and fair discrete variance strikes are derived in different models of the underlying evolution of the asset price: the Black-Scholes model, the Heston stochastic volatility model, the Merton jump-diffusion model and the Bates and Scott stochastic volatility and jump model. We determine fair discrete and continuous variance strikes analytically and fair discrete and continuous volatility strikes using simulation and variance reduction techniques and numerical integration techniques in all models. Numerical results show that the well-known convexity correction formula may not provide a good approximation of fair volatility strikes in models with jumps in the underlying asset. For realistic contract specifications and model parameters, we find that the effect of discrete sampling is typically small while the effect of jumps can be significant.

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DE GRAAF, CORNELIS S. L., QIAN FENG, DRONA KANDHAI, and CORNELIS W. OOSTERLEE. "EFFICIENT COMPUTATION OF EXPOSURE PROFILES FOR COUNTERPARTY CREDIT RISK." International Journal of Theoretical and Applied Finance 17, no. 04 (June 2014): 1450024. http://dx.doi.org/10.1142/s0219024914500241.

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Three computational techniques for approximation of counterparty exposure for financial derivatives are presented. The exposure can be used to quantify so-called Credit Valuation Adjustment (CVA) and Potential Future Exposure (PFE), which are of utmost importance for modern risk management in the financial industry, especially since the recent credit crisis. The three techniques all involve a Monte Carlo path discretization and simulation of the underlying entities. Along the generated paths, the corresponding values and distributions are computed during the entire lifetime of the option. Option values are computed by either the finite difference method for the corresponding partial differential equations, or the simulation-based Stochastic Grid Bundling Method (SGBM), or by the COS method, based on Fourier-cosine expansions. In this research, numerical results are presented for early-exercise options. The underlying asset dynamics are given by either the Black–Scholes or the Heston stochastic volatility model.

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Mehmood, Assad, Kashif Zia, Arshad Muhammad, and Dinesh Kumar Saini. "Missing observation approximation for spatio-temporal profile reconstruction in participatory sensor networks." International Journal of Crowd Science 2, no. 2 (June 11, 2018): 108–22. http://dx.doi.org/10.1108/ijcs-05-2018-0009.

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Purpose Participatory wireless sensor networks (PWSN) is an emerging paradigm that leverages existing sensing and communication infrastructures for the sensing task. Various environmental phenomenon – P monitoring applications dealing with noise pollution, road traffic, requiring spatio-temporal data samples of P (to capture its variations and its profile construction) in the region of interest – can be enabled using PWSN. Because of irregular distribution and uncontrollable mobility of people (with mobile phones), and their willingness to participate, complete spatio-temporal (CST) coverage of P may not be ensured. Therefore, unobserved data values must be estimated for CST profile construction of P and presented in this paper. Design/methodology/approach In this paper, the estimation of these missing data samples both in spatial and temporal dimension is being discussed, and the paper shows that non-parametric technique – Kernel Regression – provides better estimation compared to parametric regression techniques in PWSN context for spatial estimation. Furthermore, the preliminary results for estimation in temporal dimension have been provided. The deterministic and stochastic approaches toward estimation in the context of PWSN have also been discussed. Findings For the task of spatial profile reconstruction, it is shown that non-parametric estimation technique (kernel regression) gives a better estimation of the unobserved data points. In case of temporal estimation, few preliminary techniques have been studied and have shown that further investigations are required to find out best estimation technique(s) which may approximate the missing observations (temporally) with considerably less error. Originality/value This study addresses the environmental informatics issues related to deterministic and stochastic approaches using PWSN.

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