Journal articles: 'Stochastic processes Mathemetical models'

1

Veretennikov, Alexander. "Stochastic Processes and Models." Bulletin of the London Mathematical Society 39, no. 1 (January 16, 2007): 167–69. http://dx.doi.org/10.1112/blms/bdl020.

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Fricks, John. "Stochastic Processes and Models." Journal of the American Statistical Association 102, no. 477 (March 2007): 381. http://dx.doi.org/10.1198/jasa.2007.s166.

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Duerr, Hans-Peter, and Klaus Dietz. "Stochastic models for aggregation processes." Mathematical Biosciences 165, no. 2 (June 2000): 135–45. http://dx.doi.org/10.1016/s0025-5564(00)00014-6.

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Anh, V. V., C. C. Heyde, and Q. Tieng. "Stochastic models for fractal processes." Journal of Statistical Planning and Inference 80, no. 1-2 (August 1999): 123–35. http://dx.doi.org/10.1016/s0378-3758(98)00246-8.

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Rota, Gian-Carlo. "Stochastic models for social processes." Advances in Mathematics 57, no. 1 (July 1985): 91. http://dx.doi.org/10.1016/0001-8708(85)90110-0.

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Belopolskaya, Ya I. "Stochastic Models of Chemotaxis Processes." Journal of Mathematical Sciences 251, no. 1 (October 12, 2020): 1–14. http://dx.doi.org/10.1007/s10958-020-05059-7.

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Ebeling, W. "Stochastic models of innovation processes." Annual Review in Automatic Programming 12 (January 1985): 54–57. http://dx.doi.org/10.1016/0066-4138(85)90328-3.

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Gottinger, Hans W. "Stochastic models of oil spill processes." International Journal of Environment and Pollution 15, no. 3 (2001): 266. http://dx.doi.org/10.1504/ijep.2001.005185.

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Dijkerman, R. W., and R. R. Mazumdar. "Wavelet representations of stochastic processes and multiresolution stochastic models." IEEE Transactions on Signal Processing 42, no. 7 (July 1994): 1640–52. http://dx.doi.org/10.1109/78.298272.

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Stoyanov, Jordan. "Stochastic Processes and Models by D. Stirzaker." Journal of the Royal Statistical Society: Series A (Statistics in Society) 169, no. 4 (October 2006): 1013–14. http://dx.doi.org/10.1111/j.1467-985x.2006.00446_16.x.

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Artikis, Constantinos T., and Panagiotis T. Artikis. "Processes of educational informatics incorporating stochastic models." Journal of Interdisciplinary Mathematics 12, no. 4 (August 2009): 553–64. http://dx.doi.org/10.1080/09720502.2009.10700646.

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Pfeiffer, F., and A. Kunert. "Rattling models from deterministic to stochastic processes." Nonlinear Dynamics 1, no. 1 (January 1990): 63–74. http://dx.doi.org/10.1007/bf01857585.

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Batchelder, William H., and John P. Boyd. "Models for behavior: Stochastic processes in psychology." Journal of Mathematical Psychology 29, no. 1 (March 1985): 122–27. http://dx.doi.org/10.1016/0022-2496(85)90022-7.

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Albeverio, Sergio, and Shao-Ming Fei. "Symmetry, Integrable Chain Models and Stochastic Processes." Reviews in Mathematical Physics 10, no. 06 (August 1998): 723–50. http://dx.doi.org/10.1142/s0129055x98000239.

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A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with An symmetry and the related Temperley–Lieb algebraic structures and representations are discussed. It is shown that corresponding to these An symmetric integrable chain models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov chains with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the corresponding integrable models.

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Luschgy, Harald. "Comparison of location models for stochastic processes." Probability Theory and Related Fields 93, no. 1 (March 1992): 39–66. http://dx.doi.org/10.1007/bf01195387.

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Shiebler, Dan. "Categorical Stochastic Processes and Likelihood." Compositionality 3 (April 14, 2021): 1. http://dx.doi.org/10.32408/compositionality-3-1.

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We take a category-theoretic perspective on the relationship between probabilistic modeling and gradient based optimization. We define two extensions of function composition to stochastic process subordination: one based on a co-Kleisli category and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category of Markov kernels Stoch through a pushforward procedure.We extend stochastic processes to parametric statistical models and define a way to compose the likelihood functions of these models. We demonstrate how the maximum likelihood estimation procedure defines a family of identity-on-objects functors from categories of statistical models to the category of supervised learning algorithms Learn.Code to accompany this paper can be found on GitHub (https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood).

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Brockwell, Peter J. "Stochastic models in cell kinetics." Journal of Applied Probability 25, A (1988): 91–111. http://dx.doi.org/10.2307/3214149.

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We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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Brockwell, Peter J. "Stochastic models in cell kinetics." Journal of Applied Probability 25, A (1988): 91–111. http://dx.doi.org/10.1017/s0021900200040286.

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We discuss the role of stochastic processes in modelling the life-cycle of a biological cell and the growth of cell populations. Results for multiphase age-dependent branching processes have proved invaluable for the interpretation of many of the basic experimental studies of the life-cycle. Moreover problems from cell kinetics, in particular those related to diurnal rhythm in cell-growth, have stimulated research into ‘periodic' renewal theory, and the asymptotic behaviour of populations of cells with periodic death rate.

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Scholz, Klaus. "Stochastic simulation of urbanhydrological processes." Water Science and Technology 36, no. 8-9 (October 1, 1997): 25–31. http://dx.doi.org/10.2166/wst.1997.0639.

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Calculations in urban hydrology have almost exclusively been of deterministic character and give therefore unequivocal results. Uncertainties, which are always present, can not been eliminated by more complex models. To take uncertainties into account stochastic algorithms are integrated into hydrological components. A stochastic-hydrological method has developed which can be used to various problems. In contrast to the usual purely deterministic models the model makes it possible to get concrete information of liability of the calibration and prognosis regarding confidence limits The model is applied for the calibration and prognosis of pollutant load hydrographs. The result is, that stochastic and physical based parameters should be taken into account.

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Lee, Mei-Ling Ting, and G. Alex Whitmore. "Stochastic processes directed by randomized time." Journal of Applied Probability 30, no. 2 (June 1993): 302–14. http://dx.doi.org/10.2307/3214840.

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The paper investigates stochastic processes directed by a randomized time process. A new family of directing processes called Hougaard processes is introduced. Monotonicity properties preserved under subordination, and dependence among processes directed by a common randomized time are studied. Results for processes subordinated to Poisson and stable processes are presented. Potential applications to shock models and threshold models are also discussed. Only Markov processes are considered.

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Lee, Mei-Ling Ting, and G. Alex Whitmore. "Stochastic processes directed by randomized time." Journal of Applied Probability 30, no. 02 (June 1993): 302–14. http://dx.doi.org/10.1017/s0021900200117322.

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The paper investigates stochastic processes directed by a randomized time process. A new family of directing processes called Hougaard processes is introduced. Monotonicity properties preserved under subordination, and dependence among processes directed by a common randomized time are studied. Results for processes subordinated to Poisson and stable processes are presented. Potential applications to shock models and threshold models are also discussed. Only Markov processes are considered.

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Hasegawa, H., and H. Ezawa. "Stochastic Calculus and Some Models of Irreversible Processes." Progress of Theoretical Physics Supplement 69 (May 14, 2013): 41–54. http://dx.doi.org/10.1143/ptp.69.41.

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CARNAFFAN, SEAN. "ANOMALOUS DIFFUSION PROCESSES: STOCHASTIC MODELS AND THEIR PROPERTIES." Bulletin of the Australian Mathematical Society 101, no. 3 (March 27, 2020): 514–17. http://dx.doi.org/10.1017/s0004972720000258.

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Hughes-Oliver, Jacqueline M., and Graciela González-Farı́as. "Parametric covariance models for shock-induced stochastic processes." Journal of Statistical Planning and Inference 77, no. 1 (February 1999): 51–72. http://dx.doi.org/10.1016/s0378-3758(98)00186-4.

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DETYNA, J. "Stochastic Models of Particle Distribution in Separation Processes." Archives of Civil and Mechanical Engineering 10, no. 1 (January 2010): 15–26. http://dx.doi.org/10.1016/s1644-9665(12)60127-7.

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Holubec, Viktor, Artem Ryabov, Sarah A. M. Loos, and Klaus Kroy. "Equilibrium stochastic delay processes." New Journal of Physics 24, no. 2 (February 1, 2022): 023021. http://dx.doi.org/10.1088/1367-2630/ac4b91.

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Abstract Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is available for linear models only. We introduce a class of stochastic delay processes with nonlinear time-local forces and linear time-delayed forces that obey fluctuation theorems and converge to a Boltzmann equilibrium at long times. From the point of view of control theory, such ‘equilibrium stochastic delay processes’ are stable and energetically passive, by construction. Computationally, they provide diverse exact constraints on general nonlinear stochastic delay problems and can, in various situations, serve as a starting point for their perturbative analysis. Physically, they admit an interpretation in terms of an underdamped Brownian particle that is either subjected to a time-local force in a non-Markovian thermal bath or to a delayed feedback force in a Markovian thermal bath. We illustrate these properties numerically for a setup familiar from feedback cooling and point out experimental implications.

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Aase, Knut K. "Stochastic control of geometric processes." Journal of Applied Probability 24, no. 1 (March 1987): 97–104. http://dx.doi.org/10.2307/3214062.

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Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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Aase, Knut K. "Stochastic control of geometric processes." Journal of Applied Probability 24, no. 01 (March 1987): 97–104. http://dx.doi.org/10.1017/s0021900200030643.

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Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.

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Duong, Dam Ton, and Phung Ngoc Nguyen. "Stochastic differential of Ito – Levy processes." Science and Technology Development Journal 19, no. 2 (June 30, 2016): 80–83. http://dx.doi.org/10.32508/stdj.v19i2.792.

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In this paper, we continue to expand some results to get the product rule for differential of stochastic processes with jump, and apply for some special processes like pure jump process, Levy-Ornstein-Uhlenbeck process, geometric Levy process, in models of finance, ecomomics, and information technology.

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Pichor, Katarzyna, and Ryszard Rudnicki. "One and two-phase cell cycle models." BIOMATH 8, no. 1 (June 1, 2019): 1905261. http://dx.doi.org/10.11145/j.biomath.2019.05.261.

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In this review paper we present deterministic and stochastic one and two-phase models of the cell cycle. The deterministic models are given by partial differential equations of the first order with time delay and space variable retardation. The stochastic models are given by stochastic iterations or by piecewise deterministic Markov processes. We study asymptotic stability and sweeping of stochastic semigroups which describe the evolution of densities of these processes. We also present some results concerning chaotic behaviour of models and relations between different types of models.

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Davis, William, and Bruce Buffett. "Inferring core processes using stochastic models of the geodynamo." Geophysical Journal International 228, no. 3 (October 8, 2021): 1478–93. http://dx.doi.org/10.1093/gji/ggab412.

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SUMMARY Recent studies have represented time variations in the Earth’s axial magnetic dipole field as a stochastic process, which comprise both deterministic and random elements. To explore how these elements are affected by the style and vigour of convection in the core, as well as the core–mantle boundary conditions, we construct stochastic models from a set of numerical dynamo simulations at low Ekman numbers. The deterministic part of the stochastic model, the drift term, characterizes the slow relaxation of the dipole back to its time average. We find that these variations are predominantly accommodated by the slowest decay mode, enhanced by turbulent diffusion to enable a faster relaxation. The random part—the noise term—is set by the amplitude and timescale of variations in dipole field generation, including contributions from both velocity and internal magnetic field variations. Applying these interpretations to the palaeomagnetic field suggest that reversal rates are very sensitive to rms variations in the field generation. Less than a 50 per cent reduction in rms field generation variations is sufficient to prevent reversals for the recent magnetic field.

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Aslanov, A. M., A. N. Herega, and T. L. Lozovskiĭ. "Two models of stochastic processes in centrifugal feedback filters." Technical Physics 51, no. 6 (June 2006): 812–13. http://dx.doi.org/10.1134/s1063784206060211.

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Leithead, W. E., Kian Seng Neo, and D. J. Leith. "GAUSSIAN REGRESSION BASED ON MODELS WITH TWO STOCHASTIC PROCESSES." IFAC Proceedings Volumes 38, no. 1 (2005): 142–47. http://dx.doi.org/10.3182/20050703-6-cz-1902.00024.

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Diosi, L. "Quantum stochastic processes as models for state vector reduction." Journal of Physics A: Mathematical and General 21, no. 13 (July 7, 1988): 2885–98. http://dx.doi.org/10.1088/0305-4470/21/13/013.

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Mattos, César Lincoln C., and Guilherme A. Barreto. "A stochastic variational framework for Recurrent Gaussian Processes models." Neural Networks 112 (April 2019): 54–72. http://dx.doi.org/10.1016/j.neunet.2019.01.005.

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Jaeger, Herbert. "Observable Operator Models for Discrete Stochastic Time Series." Neural Computation 12, no. 6 (June 1, 2000): 1371–98. http://dx.doi.org/10.1162/089976600300015411.

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A widely used class of models for stochastic systems is hidden Markov models. Systems that can be modeled by hidden Markov models are a proper subclass of linearly dependent processes, a class of stochastic systems known from mathematical investigations carried out over the past four decades. This article provides a novel, simple characterization of linearly dependent processes, called observable operator models. The mathematical properties of observable operator models lead to a constructive learning algorithm for the identification of linearly dependent processes. The core of the algorithm has a time complexity of O (N + nm3), where N is the size of training data, n is the number of distinguishable outcomes of observations, and m is model state-space dimension.

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Hwan Cha, Ji, and Sophie Mercier. "Transformed Lévy processes as state-dependent wear models." Advances in Applied Probability 51, no. 2 (June 2019): 468–86. http://dx.doi.org/10.1017/apr.2019.21.

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AbstractMany wear processes used for modeling accumulative deterioration in a reliability context are nonhomogeneous Lévy processes and, hence, have independent increments, which may not be suitable in an application context. In this work we consider Lévy processes transformed by monotonous functions to overcome this restriction, and provide a new state-dependent wear model. These transformed Lévy processes are first observed to remain tractable Markov processes. Some distributional properties are derived. We investigate the impact of the current state on the future increment level and on the overall accumulated level from a stochastic monotonicity point of view. We also study positive dependence properties and stochastic monotonicity of increments.

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Comte, F., and E. Renault. "Noncausality in Continuous Time Models." Econometric Theory 12, no. 2 (June 1996): 215–56. http://dx.doi.org/10.1017/s0266466600006575.

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In this paper, we study new definitions of noncausality, set in a continuous time framework, illustrated by the intuitive example of stochastic volatility models. Then, we define CIMA processes (i.e., processes admitting a continuous time invertible moving average representation), for which canonical representations and sufficient conditions of invertibility are given. We can provide for those CIMA processes parametric characterizations of noncausality relations as well as properties of interest for structural interpretations. In particular, we examine the example of processes solutions of stochastic differential equations, for which we study the links between continuous and discrete time definitions, find conditions to solve the possible problem of aliasing, and set the question of testing continuous time noncausality on a discrete sample of observations. Finally, we illustrate a possible generalization of definitions and characterizations that can be applied to continuous time fractional ARMA processes.

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Wilks, Daniel S. "Effects of stochastic parametrization on conceptual climate models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1875 (April 29, 2008): 2475–88. http://dx.doi.org/10.1098/rsta.2008.0005.

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Conceptual climate models are very simple mathematical representations of climate processes, which are especially useful because their workings can be readily understood. The usual procedure of representing effects of unresolved processes in such models using functions of the prognostic variables (parametrizations) that include no randomness generally results in these models exhibiting substantially less variability than do the phenomena they are intended to simulate. A viable yet still simple alternative is to replace the conventional deterministic parametrizations with stochastic parametrizations, which can be justified theoretically through the central limit theorem. The result is that the model equations are stochastic differential equations. In addition to greatly increasing the magnitude of variability exhibited by these models, and their qualitative fidelity to the corresponding real climate system, representation of unresolved influences by random processes can allow these models to exhibit surprisingly rich new behaviours of which their deterministic counterparts are incapable.

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Console, Rodolfo, Maura Murru, and Flaminia Catalli. "Physical and stochastic models of earthquake clustering." Tectonophysics 417, no. 1-2 (April 2006): 141–53. http://dx.doi.org/10.1016/j.tecto.2005.05.052.

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Pouliasis, George, Gina Alexandra Torres-Alves, and Oswaldo Morales-Napoles. "Stochastic Modeling of Hydroclimatic Processes Using Vine Copulas." Water 13, no. 16 (August 5, 2021): 2156. http://dx.doi.org/10.3390/w13162156.

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The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto- and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated.

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Gwiżdż, Piotr. "Applications of Stochastic Semigroups to Queueing Models." Annales Mathematicae Silesianae 33, no. 1 (September 1, 2019): 121–42. http://dx.doi.org/10.2478/amsil-2018-0007.

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AbstractNon-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of variables and non-local boundary conditions. We show how one can study such systems by using the theory of stochastic semigroups.

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Stirzaker, David. "PROCESSES WITH RANDOM REGULATION." Probability in the Engineering and Informational Sciences 21, no. 1 (December 15, 2006): 1–17. http://dx.doi.org/10.1017/s0269964807070015.

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We consider a class of stochastic models for systems subject to random regulation. We derive expressions for the distribution of the intervals between regulating instants and for the transient and equilibrium properties of the process. Some of these are evaluated explicitly for some models of interest.

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YAMAZAKI, AKIRA. "ON VALUATION WITH STOCHASTIC PROPORTIONAL HAZARD MODELS IN FINANCE." International Journal of Theoretical and Applied Finance 16, no. 03 (May 2013): 1350017. http://dx.doi.org/10.1142/s0219024913500179.

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While the proportional hazard model is recognized to be statistically meaningful for analyzing and estimating financial event risks, the existing literature that analytically deals with the valuation problems is very limited. In this paper, adopting the proportional hazard model in continuous time setting, we provide an analytical treatment for the valuation problems. The derived formulas, which are based on the generalized Edgeworth expansion and give approximate solutions to the valuation problems, are widely useful for evaluating a variety of financial products such as corporate bonds, credit derivatives, mortgage-backed securities, saving accounts and time deposits. Furthermore, the formulas are applicable to the proportional hazard model having not only continuous processes (e.g., Gaussian, affine, and quadratic Gaussian processes) but also discontinuous processes (e.g., Lévy and time-changed Lévy processes) as stochastic covariates. Through numerical examples, it is demonstrated that very accurate values can be quickly obtained by the formulas such as a closed-form formula.

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Rønn-Nielsen, Anders, Jon Sporring, and Eva B. Vedel Jensen. "ESTIMATION OF SAMPLE SPACING IN STOCHASTIC PROCESSES." Image Analysis & Stereology 36, no. 1 (March 31, 2017): 43. http://dx.doi.org/10.5566/ias.1681.

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Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Lévy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies.

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Mikosch, Thomas, Gennady Samorodnitsky, and Murad S. Taqqu. "Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance." Journal of the American Statistical Association 90, no. 430 (June 1995): 805. http://dx.doi.org/10.2307/2291104.

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Linde, W. "STABLE NON-GAUSSIAN RANDOM PROCESSES: STOCHASTIC MODELS WITH INFINITE VARIANCE." Bulletin of the London Mathematical Society 28, no. 5 (September 1996): 554–56. http://dx.doi.org/10.1112/blms/28.5.554.

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Kawamura, Toshihiko, and Yasumasa Saisho. "Stochastic Models Describing Human Metabolic Processes Using SDEs with Reflection." Stochastic Models 22, no. 2 (July 2006): 273–87. http://dx.doi.org/10.1080/15326340600649037.

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Champagnat, Nicolas, Régis Ferrière, and Sylvie Méléard. "From Individual Stochastic Processes to Macroscopic Models in Adaptive Evolution." Stochastic Models 24, sup1 (November 5, 2008): 2–44. http://dx.doi.org/10.1080/15326340802437710.

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Champagnat, Nicolas, Régis Ferrière, and Sylvie Méléard. "Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models." Theoretical Population Biology 69, no. 3 (May 2006): 297–321. http://dx.doi.org/10.1016/j.tpb.2005.10.004.

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Journal articles on the topic 'Stochastic processes Mathemetical models'

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