Thematische Bibliographien / Stochastic Differential Equations (SDE)

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Auswahl der wissenschaftlichen Literatur zum Thema „Stochastic Differential Equations (SDE)“

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Veröffentlicht am 1. Februar 2025

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Zeitschriftenartikel zum Thema "Stochastic Differential Equations (SDE)"

Eliazar, Iddo. „Selfsimilar stochastic differential equations“. Europhysics Letters 136, Nr. 4 (01.11.2021): 40002. http://dx.doi.org/10.1209/0295-5075/ac4dd4.

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Abstract Diffusion in a logarithmic potential (DLP) attracted significant interest in physics recently. The dynamics of DLP are governed by a Langevin stochastic differential equation (SDE) whose underpinning potential is logarithmic, and that is driven by Brownian motion. The SDE that governs DLP is a particular case of a selfsimilar SDE: one that is driven by a selfsimilar motion, and that produces a selfsimilar motion. This paper establishes the pivotal role of selfsimilar SDEs via two novel universality results. I) Selfsimilar SDEs emerge universally, on the macro level, when applying scaling limits to micro-level SDEs. II) Selfsimilar SDEs emerge universally when applying the Lamperti transformation to stationary SDEs. Using the universality results, this paper further establishes: a novel statistical-analysis approach to selfsimilar Ito diffusions; and the focal importance of DLP.

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Iddrisu, Wahab A., Inusah Iddrisu und Abdul-Karim Iddrisu. „Modeling Cholera Epidemiology Using Stochastic Differential Equations“. Journal of Applied Mathematics 2023 (09.05.2023): 1–17. http://dx.doi.org/10.1155/2023/7232395.

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In this study, we extend Codeço’s classical SI-B epidemic and endemic model from a deterministic framework into a stochastic framework. Then, we formulated it as a stochastic differential equation for the number of infectious individuals I t under the role of the aquatic environment. We also proved that this stochastic differential equation (SDE) exists and is unique. The reproduction number, R 0 , was derived for the deterministic model, and qualitative features such as the positivity and invariant region of the solution, the two equilibrium points (disease-free and endemic equilibrium), and stabilities were studied to ensure the biological meaningfulness of the model. Numerical simulations were also carried out for the stochastic differential equation (SDE) model by utilizing the Euler-Maruyama numerical method. The method was used to simulate the sample path of the SI-B stochastic differential equation for the number of infectious individuals I t , and the findings showed that the sample path or trajectory of the stochastic differential equation for the number of infectious individuals I t is continuous but not differentiable and that the SI-B stochastic differential equation model for the number of infectious individuals I t fluctuates inside the solution of the SI-B ordinary differential equation model. Another significant feature of our proposed SDE model is its simplicity.

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IMKELLER, PETER, und CHRISTIAN LEDERER. „THE COHOMOLOGY OF STOCHASTIC AND RANDOM DIFFERENTIAL EQUATIONS, AND LOCAL LINEARIZATION OF STOCHASTIC FLOWS“. Stochastics and Dynamics 02, Nr. 02 (Juni 2002): 131–59. http://dx.doi.org/10.1142/s021949370200039x.

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Random dynamical systems can be generated by stochastic differential equations (sde) on the one hand, and by random differential equations (rde), i.e. randomly parametrized ordinary differential equations on the other hand. Due to conflicting concepts in stochastic calculus and ergodic theory, asymptotic problems for systems associated with sde are harder to treat. We show that both objects are basically identical, modulo a stationary coordinate change (cohomology) on the state space. This observation opens completely new opportunities for the treatment of asymptotic problems for systems related to sde: just study them for the conjugate rde, which is often possible by simple path-by-path classical arguments. This is exemplified for the problem of local linearization of random dynamical systems, the classical analogue of which leads to the Hartman–Grobman theorem.

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Briand, Phillippe, Abir Ghannoum und Céline Labart. „Mean reflected stochastic differential equations with jumps“. Advances in Applied Probability 52, Nr. 2 (Juni 2020): 523–62. http://dx.doi.org/10.1017/apr.2020.11.

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AbstractIn this paper, a reflected stochastic differential equation (SDE) with jumps is studied for the case where the constraint acts on the law of the solution rather than on its paths. These reflected SDEs have been approximated by Briand et al. (2016) using a numerical scheme based on particles systems, when no jumps occur. The main contribution of this paper is to prove the existence and the uniqueness of the solutions to this kind of reflected SDE with jumps and to generalize the results obtained by Briand et al. (2016) to this context.

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Armstrong, J., und D. Brigo. „Intrinsic stochastic differential equations as jets“. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, Nr. 2210 (Februar 2018): 20170559. http://dx.doi.org/10.1098/rspa.2017.0559.

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We explain how Itô stochastic differential equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We also show how jets can be used to derive graphical representations of Itô SDEs, and we show how jets can be used to derive the differential operators associated with SDEs in a coordinate-free manner. We relate jets to vector flows, giving a geometric interpretation of the Itô–Stratonovich transformation. We show how percentiles can be used to give an alternative coordinate-free interpretation of the coefficients of one-dimensional SDEs. We relate this to the jet approach. This allows us to interpret the coefficients of SDEs in terms of ‘fan diagrams’. In particular, the median of an SDE solution is associated with the drift of the SDE in Stratonovich form for small times.

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Bahlali, K., A. Elouaflin und M. N'zi. „Backward stochastic differential equations with stochastic monotone coefficients“. Journal of Applied Mathematics and Stochastic Analysis 2004, Nr. 4 (01.01.2004): 317–35. http://dx.doi.org/10.1155/s1048953304310038.

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We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in a Markovian framework, that is coupled with a forward SDE, our result provides a probabilistic interpretation of solutions to nonlinear PDEs.

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Rezaeyan, Ramzan. „Application of Stochastic Differential Equation and Optimal Control for Engineering Problems“. Advanced Materials Research 383-390 (November 2011): 972–75. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.972.

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Stochastic differential equations(SDEs) is fundamental for the modeling in engineering and science. The goal of this paper is study optimal control of the solution a SDE. We consider the optimal control for risky stocks stochastic model with using of the SDE.

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Fekete, Dorottya, Joaquin Fontbona und Andreas E. Kyprianou. „Skeletal stochastic differential equations for superprocesses“. Journal of Applied Probability 57, Nr. 4 (23.11.2020): 1111–34. http://dx.doi.org/10.1017/jpr.2020.53.

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AbstractIt is well understood that a supercritical superprocess is equal in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which initiates subcritical superprocesses. The Markov branching process corresponds to the genealogical description of prolific individuals, that is, individuals who produce eternal genealogical lines of descent, and is often referred to as the skeleton or backbone of the original superprocess. The Poissonian dressing along the skeleton may be considered to be the remaining non-prolific genealogical mass in the superprocess. Such skeletal decompositions are equally well understood for continuous-state branching processes (CSBP).In a previous article [16] we developed an SDE approach to study the skeletal representation of CSBPs, which provided a common framework for the skeletal decompositions of supercritical and (sub)critical CSBPs. It also helped us to understand how the skeleton thins down onto one infinite line of descent when conditioning on survival until larger and larger times, and eventually forever.Here our main motivation is to show the robustness of the SDE approach by expanding it to the spatial setting of superprocesses. The current article only considers supercritical superprocesses, leaving the subcritical case open.

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Stoyanov, Jordan, und Dobrin Botev. „Quantitative results for perturbed stochastic differential equations“. Journal of Applied Mathematics and Stochastic Analysis 9, Nr. 3 (01.01.1996): 255–61. http://dx.doi.org/10.1155/s104895339600024x.

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The paper is devoted to Itô type stochastic differential equations (SDE's) with small perturbations. Our goal is to present strong results showing how close are the 2m-order moments of the solutions of the perturbed SDE's and the unperturbed SDE.

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Chaharpashlou, Reza, Reza Saadati und António M. Lopes. „Fuzzy Mittag–Leffler–Hyers–Ulam–Rassias Stability of Stochastic Differential Equations“. Mathematics 11, Nr. 9 (04.05.2023): 2154. http://dx.doi.org/10.3390/math11092154.

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Stability is the most relevant property of dynamical systems. The stability of stochastic differential equations is a challenging and still open problem. In this article, using a fuzzy Mittag–Leffler function, we introduce a new fuzzy controller function to stabilize the stochastic differential equation (SDE) ν′(γ,μ)=Fγ,μ,ν(γ,μ). By adopting the fixed point technique, we are able to prove the fuzzy Mittag–Leffler–Hyers–Ulam–Rassias stability of the SDE.

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Dissertationen zum Thema "Stochastic Differential Equations (SDE)"

Nass, Aminu Ma'aruf. „Point symmetry methods for Itô Stochastic Differential Equations (SDE) with a finite jump process“. Doctoral thesis, University of Cape Town, 2017. http://hdl.handle.net/11427/25387.

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The mixture of Wiener and a Poisson processes are the primary tools used in creating jump-diffusion process which is very popular in mathematical modeling. In financial mathematics, they are used to describe the change of stock rates and bonanzas, and they are often used in mathematical biology modeling and population dynamics. In this thesis, we extended the Lie point symmetry theory of deterministic differential equations to the class of jump-diffusion stochastic differential equations, i.e., a stochastic process driven by both Wiener and Poisson processes. The Poisson process generates the jumps whereas the Brownian motion path is continuous. The determining equations for a stochastic differential equation with finite jump are successfully derived in an Itô calculus context and are found to be deterministic, even though they represent a stochastic process. This work leads to an understanding of the random time change formulae for Poisson driven process in the context of Lie point symmetries without having to consult much of the intense Itô calculus theory needed to formally derive it. We apply the invariance methodology of Lie point transformation together with the more generalized Itô formulae, without enforcing any conditions to the moments of the stochastic processes to derive the determining equations and apply it to few models. In the first part of the thesis, point symmetry of Poisson-driven stochastic differential equations is discussed, by considering the infinitesimals of not only spatial and temporal variables but also infinitesimals of the Poisson process variable. This was later extended, in the second part, to define the symmetry of jumpdiffusion stochastic differential equations (i.e., stochastic differential equations driven by both Wiener and Poisson processes).

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Handari, Bevina D. „Numerical methods for SDEs and their dynamics /“. [St. Lucia, Qld.], 2002. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17145.pdf.

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Salhi, Rym. „Contributions to quadratic backward stochastic differential equations with jumps and applications“. Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1023.

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Cette thèse porte sur l'étude des équations différentielles stochastiques rétrogrades (EDSR) avec sauts et leurs applications.Dans le chapitre 1, nous étudions une classe d'EDSR lorsque le bruit provient d'un mouvement Brownien et d'une mesure aléatoire de saut indépendante à activité infinie. Plus précisément, nous traitons le cas où le générateur est à croissance quadratique et la condition terminale est non bornée. L'existence et l'unicité de la solution sont prouvées en combinant à la fois la procédure d'approximation monotone et une approche progressive. Cette méthode permet de résoudre le cas où la condition terminale est non bornée.Le chapitre 2 est consacré aux EDSR avec sauts généralisées doublement réfléchies sous des hypothèses d’intégrabilités faibles. Plus précisément, on montre l'existence d'une solution pour un générateur à croissance quadratique stochastique et une condition terminale non bornée. Nous montrons également, dans un cadre approprié, la connexion entre notre classe d’équations différentielles stochastiques rétrogrades et les jeu à somme nuls.Dans le chapitre 3, nous considérons une classe générale d'EDSR progressive-rétrograde couplée avec sauts de type Mackean Vlasov sous une condition faible de monotonicité. Les résultats d'existence et d'unicité sont établis sous deux classes d'hypothèses en se basant sur des schémas de perturbations soit de l’équation différentielle stochastique progressive, soit de l’équation différentielle stochastique rétrograde. On conclut le chapitre par un problème de stockage optimal d’énergie dans un parc électrique de type champs moyen
This thesis focuses on backward stochastic differential equation with jumps and their applications. In the first chapter, we study a backward stochastic differential equation (BSDE for short) driven jointly by a Brownian motion and an integer valued random measure that may have infinite activity with compensator being possibly time inhomogeneous. In particular, we are concerned with the case where the driver has quadratic growth and unbounded terminal condition. The existence and uniqueness of the solution are proven by combining a monotone approximation technics and a forward approach. Chapter 2 is devoted to the well-posedness of generalized doubly reflected BSDEs (GDRBSDE for short) with jumps under weaker assumptions on the data. In particular, we study the existence of a solution for a one-dimensional GDRBSDE with jumps when the terminal condition is only measurable with respect to the related filtration and when the coefficient has general stochastic quadratic growth. We also show, in a suitable framework, the connection between our class of backward stochastic differential equations and risk sensitive zero-sum game. In chapter 3, we investigate a general class of fully coupled mean field forward-backward under weak monotonicity conditions without assuming any non-degeneracy assumption on the forward equation. We derive existence and uniqueness results under two different sets of conditions based on proximation schema weither on the forward or the backward equation. Later, we give an application for storage in smart grids

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Alnafisah, Yousef Ali. „First-order numerical schemes for stochastic differential equations using coupling“. Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20420.

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We study a new method for the strong approximate solution of stochastic differential equations using coupling and we prove order one error bounds for the new scheme in Lp space assuming the invertibility of the diffusion matrix. We introduce and implement two couplings called the exact and approximate coupling for this scheme obtaining good agreement with the theoretical bound. Also we describe a method for non-invertibility case (Combined method) and we investigate its convergence order which will give O(h3/4 √log(h)j) under some conditions. Moreover we compare the computational results for the combined method with its theoretical error bound and we have obtained a good agreement between them. In the last part of this thesis we work out the performance of the multilevel Monte Carlo method using the new scheme with the exact coupling and we compare the results with the trivial coupling for the same scheme.

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Manai, Arij. „Some contributions to backward stochastic differential equations and applications“. Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1022.

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Cette thèse est consacrée à l'étude des équations différentielles stochastiques rétrogrades (EDSR) et leurs applications. Dans le chapitre 1, on étudie le problème de maximisation de l'utilité de la richesse terminale où le prix de l'actif peut être discontinue sous des contraintes sur les stratégies de l'agent. Nous nous concentrons sur l'EDSR dont la solution représente l'utilité maximale, ce qui permet de transférer des résultats sur les EDSR quadratiques, en particulier les résultats de stabilité, au problème de maximisation d'utilité. Dans le chapitre 2, nous considèrons le problème de valorisation d'options Américaines des points de vue théorique et numérique en s'appuyant sur la représentation du prix de l'option comme solution de viscosité d'une équation parabolique non linéaire. Nous étendons le résultat prouvé dans [Benth, Karlsen and Reikvam 2003] pour un put ou call Américain à un cas plus général dans un cadre multidimensionnel. Nous proposons deux schémas numériques inspirés par les processus de branchement. Nos expériences numériques montrent que l'approximation du générateur discontinu, associé à l'EDP, par des polynômes locaux n'est pas efficace tandis qu'une simple procédure de randomisation donne de très bon résultats. Dans le chapitre 3, nous prouvons des résultats d'existence et d'unicité pour une classe générale d'équations progressives-rétrogrades à champs moyen sous une condition de monotonicité faible et une hypothèse non-dégénérescence sur l'équation progressive et nous donnons une application dans le domaine de stockage d'énergie dans le cas où la production d'électricité est imprévisible
This thesis is dedicated to the study of backward stochastic differential equations (BSDEs) and their applications. In chapter 1, we study the problem of maximizing the utility from terminal wealth where the stock price may jump and there are investment constraints on the agent 's strategies. We focus on the BSDE whose solution represents the maximal utility, which allows transferring results on quadratic BSDEs, in particular the stability results, to the problem of utility maximisation. In chapter 2, we consider the problem of pricing American options from theoretical and numerical sides based upon an alternative representation of the value of the option in the form of a viscosity solution of a parabolic equation with a nonlinear reaction term. We extend the viscosity solution characterization proved in [Benth, Karlsen and Reikvam 2003] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting. We address two new numerical schemes inspired by the branching processes. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results. In chapter 3, we prove existence and uniqueness results for a general class of coupled mean-field forward-backward SDEs with jumps under weak monotonicity conditions and without the non-degeneracy assumption on the forward equation and we give an application in the field of storage in smart grids in the case where the production of electricity is unpredictable

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Leahy, James-Michael. „On parabolic stochastic integro-differential equations : existence, regularity and numerics“. Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10569.

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In this thesis, we study the existence, uniqueness, and regularity of systems of degenerate linear stochastic integro-differential equations (SIDEs) of parabolic type with adapted coefficients in the whole space. We also investigate explicit and implicit finite difference schemes for SIDEs with non-degenerate diffusion. The class of equations we consider arise in non-linear filtering of semimartingales with jumps. In Chapter 2, we derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by Lévy driven stochastic differential equations (SDEs) with adapted coefficients in weighted Hölder norms using the Sobolev embedding theorem and the change of variable formula. As an application of some basic properties of flows of Weiner driven SDEs, we prove the existence and uniqueness of classical solutions of linear parabolic second order stochastic partial differential equations (SPDEs) by partitioning the time interval and passing to the limit. The methods we use allow us to improve on previously known results in the continuous case and to derive new ones in the jump case. Chapter 3 is dedicated to the proof of existence and uniqueness of classical solutions of degenerate SIDEs using the method of stochastic characteristics. More precisely, we use Feynman-Kac transformations, conditioning, and the interlacing of space inverses of stochastic flows generated by SDEs with jumps to construct solutions. In Chapter 4, we prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework of stochastic evolution equations and the method of vanishing viscosity. As an application, we establish the existence and uniqueness of solutions of degenerate linear stochastic integro-differential equations in the L2-Sobolev scale. Finite difference schemes for non-degenerate SIDEs are considered in Chapter 5. Specifically, we study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear SIDEs and show that the rate is of order one in space and order one-half in time.

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Yannios, Nicholas, und mikewood@deakin edu au. „Computational aspects of the numerical solution of SDEs“. Deakin University. School of Computing and Mathematics, 2001. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20060817.123449.

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In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

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Todeschi, Tiziano. „Calibration of local-stochastic volatility models with neural networks“. Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23052/.

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During the last twenty years several models have been proposed to improve the classic Black-Scholes framework for equity derivatives pricing. Recently a new model has been proposed: Local-Stochastic Volatility Model (LSV). This model considers volatility as the product between a deterministic and a stochastic term. So far, the model choice was not only driven by the capacity of capturing empirically observed market features well, but also by the computational tractability of the calibration process. This is now undergoing a big change since machine learning technologies offer new perspectives on model calibration. In this thesis we consider the calibration problem to be the search for a model which generates given market prices and where additionally technology from generative adversarial networks can be used. This means parametrizing the model pool in a way which is accessible for machine learning techniques and interpreting the inverse problems a training task of a generative network, whose quality is assessed by an adversary. The calibration algorithm proposed for LSV models use as generative models so-called neural stochastic differential equations (SDE), which just means to parameterize the drift and volatility of an Ito-SDE by neural networks.

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Herdiana, Ratna. „Numerical methods for SDEs - with variable stepsize implementation /“. [St. Lucia, Qld.], 2003. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe17638.pdf.

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Yue, Wen. „Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs“. Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html.

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This thesis consists of four parts. In the first part we recall some background theory that will be used throughout the thesis. In the second part, we studied the absolute continuity of the laws of the solutions of some perturbed stochastic differential equaitons(SDEs) and perturbed reflected SDEs using Malliavin calculus. Because the extra terms in the perturbed SDEs involve the maximum of the solution itself, the Malliavin differentiability of the solutions becomes very delicate. In the third part, we studied the absolute continuity of the laws of the solutions of the parabolic stochastic partial differential equations(SPDEs) with two reflecting walls using Malliavin calculus. Our study is based on Yang and Zhang \cite{YZ1}, in which the existence and uniqueness of the solutions of such SPDEs was established. In the fourth part, we gave the existence and uniqueness of the solutions of the elliptic SPDEs with two reflecting walls and general diffusion coefficients.

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Bücher zum Thema "Stochastic Differential Equations (SDE)"

Pardoux, Etienne, und Aurel Rӑşcanu. Stochastic Differential Equations, Backward SDEs, Partial Differential Equations. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05714-9.

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Kloeden, Peter E. Numerical solution of SDE through computer experiments. 2. Aufl. Berlin: Springer, 1997.

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Øksendal, Bernt. Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02847-6.

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Øksendal, Bernt. Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-662-03185-8.

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Øksendal, Bernt. Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-14394-6.

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Panik, Michael J. Stochastic Differential Equations. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119377399.

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Øksendal, Bernt. Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-13050-6.

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Øksendal, Bernt. Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-02574-1.

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Sobczyk, Kazimierz. Stochastic Differential Equations. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3712-6.

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Cecconi, Jaures, Hrsg. Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-11079-5.

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Buchteile zum Thema "Stochastic Differential Equations (SDE)"

Hassler, Uwe. „Stochastic Differential Equations (SDE)“. In Stochastic Processes and Calculus, 261–83. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-23428-1_12.

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Kim, Jin Won, und Sebastian Reich. „On Forward–Backward SDE Approaches to Conditional Estimation“. In Mathematics of Planet Earth, 115–36. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-70660-8_6.

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AbstractIn this chapter, we investigate the representation of conditional expectation values for partially observed diffusion processes in terms of appropriate estimators. The work of Kalman and Bucy has established a duality between filtering and estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an optimization problem constrained by a backward stochastic partial differential equation. Here we revisit this problem from the perspective of appropriate forward-backward stochastic differential equations. Our approach sheds new light on the conditional estimation problem and provides a unifying perspective. It is also demonstrated that certain formulations of the estimation problem lead to deterministic formulations similar to the linear Gaussian case as originally investigated by Kalman and Bucy. Finally, we discuss an application of the proposed formulation to optimal control problem on partially observed diffusion processes.

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Zhang, Jianfeng. „Reflected Backward SDEs“. In Backward Stochastic Differential Equations, 133–60. New York, NY: Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7256-2_6.

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Zhang, Jianfeng. „Forward-Backward SDEs“. In Backward Stochastic Differential Equations, 177–201. New York, NY: Springer New York, 2017. http://dx.doi.org/10.1007/978-1-4939-7256-2_8.

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Breda, Dimitri, Jung Kyu Canci und Raffaele D’Ambrosio. „An Invitation to Stochastic Differential Equations in Healthcare“. In Quantitative Models in Life Science Business, 97–110. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-11814-2_6.

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AbstractAn important problem in finance is the evaluation of the value in the future of assets (e.g., shares in company, currencies, derivatives, patents). The change of the values can be modeled with differential equations. Roughly speaking, a typical differential equation in finance has two components, one deterministic (e.g., rate of interest of bank accounts) and one stochastic (e.g., values of stocks) that is often related to the notion of Brownian motions. The solution of such a differential equation needs the evaluation of Riemann–Stieltjes’s integrals for the deterministic part and Ito’s integrals for the stochastic part. For A few types of such differential equations, it is possible to determine an exact solution, e.g., a geometric Brownian motion. On the other side for almost all stochastic differential equations we can only provide approximations of a solution. We present some numerical methods for solving stochastic differential equations.

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Liu, Wei, und Michael Röckner. „SDEs in Finite Dimensions“. In Stochastic Partial Differential Equations: An Introduction, 55–68. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22354-4_3.

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Liu, Wei, und Michael Röckner. „SDEs in Infinite Dimensions and Applications to SPDEs“. In Stochastic Partial Differential Equations: An Introduction, 69–121. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22354-4_4.

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Bruned, Y., I. Chevyrev und P. K. Friz. „Examples of Renormalized SDEs“. In Stochastic Partial Differential Equations and Related Fields, 303–17. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74929-7_19.

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Chassagneux, Jean-François, Hinesh Chotai und Mirabelle Muûls. „Introduction to Forward-Backward Stochastic Differential Equations“. In A Forward-Backward SDEs Approach to Pricing in Carbon Markets, 11–42. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63115-8_2.

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Kohatsu-Higa, Arturo, und Atsushi Takeuchi. „Flows Associated with Stochastic Differential Equations with Jumps“. In Jump SDEs and the Study of Their Densities, 145–54. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9741-8_7.

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Konferenzberichte zum Thema "Stochastic Differential Equations (SDE)"

Sul, Jinhwan, Jungin E. Kim und Yan Wang. „Quantum Functional Expansion to Solve Stochastic Differential Equations“. In 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), 552–59. IEEE, 2024. https://doi.org/10.1109/qce60285.2024.00071.

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He, Li, Qi Meng, Wei Chen, Zhi-Ming Ma und Tie-Yan Liu. „Differential Equations for Modeling Asynchronous Algorithms“. In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/307.

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Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the discrete view has its intrinsic limitations: there is no characterizationof the optimization path and the proof techniques are induction-based and thus usually complicated. Inspired by the recent successful adoptions of stochastic differential equations (SDE) to the theoretical analysis of SGD, in this paper, we study the continuous approximation of ASGD by using stochastic differential delay equations (SDDE). We introduce the approximation method and study the approximation error. Then we conduct theoretical analysis on the convergence rate of ASGD algorithm based on the continuous approximation.There are two methods: moment estimation and energy function minimization can be used to analyzethe convergence rates. Moment estimation depends on the specific form of the loss function, while energy function minimization only leverages the convex property of the loss function, and does not depend on its specific form. In addition to the convergence analysis, the continuous view also helps us derive better convergence rates. All of this clearly shows the advantage of taking the continuous view in gradient descent algorithms.

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Mukherjee, Arpan, Rahul Rai, Puneet Singla, Tarunraj Singh und Abani Patra. „An Adaptive Gaussian Mixture Model Approach Based Framework for Solving Fokker-Planck Kolmogorov Equation Related to High Dimensional Dynamical Systems“. In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60312.

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Engineering systems are often modeled as a large dimensional random process with additive noise. The analysis of such system involves a solution to simultaneous system of Stochastic Differential Equations (SDE). The exact solution to the SDE is given by the evolution of the probability density function (pdf) of the state vector through the application of Stochastic Calculus. The Fokker-Planck-Kolmogorov Equation (FPKE) provides approximate solution to the SDE by giving the time evolution equation for the non-Gaussian pdf of the state vector. In this paper, we outline a computational framework that combines linearization, clustering technique and the Adaptive Gaussian Mixture Model (AGMM) methodology for solving the Fokker-Planck-Kolmogorov Equation (FPKE) related to a high dimensional system. The linearization and clustering technique facilitate easier decomposition of the overall high dimensional FPKE system into a finite number of much lower dimension FPKE systems. The decomposition enables the solution method to be faster. Numerical simulations test the efficacy of our developed framework.

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Wang, Yan. „Simulating Stochastic Diffusions by Quantum Walks“. In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12739.

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Stochastic differential equation (SDE) and Fokker-Planck equation (FPE) are two general approaches to describe the stochastic drift-diffusion processes. Solving SDEs relies on the Monte Carlo samplings of individual system trajectory, whereas FPEs describe the time evolution of overall distributions via path integral alike methods. The large state space and required small step size are the major challenges of computational efficiency in solving FPE numerically. In this paper, a generic continuous-time quantum walk formulation is developed to simulate stochastic diffusion processes. Stochastic diffusion in one-dimensional state space is modeled as the dynamics of an imaginary-time quantum system. The proposed quantum computational approach also drastically accelerates the path integrals with large step sizes. The new approach is compared with the traditional path integral method and the Monte Carlo trajectory sampling.

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Jha, Sumit, Rickard Ewetz, Alvaro Velasquez und Susmit Jha. „On Smoother Attributions using Neural Stochastic Differential Equations“. In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/73.

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Several methods have recently been developed for computing attributions of a neural network's prediction over the input features. However, these existing approaches for computing attributions are noisy and not robust to small perturbations of the input. This paper uses the recently identified connection between dynamical systems and residual neural networks to show that the attributions computed over neural stochastic differential equations (SDEs) are less noisy, visually sharper, and quantitatively more robust. Using dynamical systems theory, we theoretically analyze the robustness of these attributions. We also experimentally demonstrate the efficacy of our approach in providing smoother, visually sharper and quantitatively robust attributions by computing attributions for ImageNet images using ResNet-50, WideResNet-101 models and ResNeXt-101 models.

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Leung, Chin-wing, Shuyue Hu und Ho-fung Leung. „Modelling the Dynamics of Multi-Agent Q-learning: The Stochastic Effects of Local Interaction and Incomplete Information“. In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/55.

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The theoretical underpinnings of multiagent reinforcement learning has recently attracted much attention. In this work, we focus on the generalized social learning (GSL) protocol --- an agent interaction protocol that is widely adopted in the literature, and aim to develop an accurate theoretical model for the Q-learning dynamics under this protocol. Noting that previous models fail to characterize the effects of local interactions and incomplete information that arise from GSL, we model the Q-values dynamics of each individual agent as a system of stochastic differential equations (SDE). Based on the SDE, we express the time evolution of the probability density function of Q-values in the population with a Fokker-Planck equation. We validate the correctness of our model through extensive comparisons with agent-based simulation results across different types of symmetric games. In addition, we show that as the interactions between agents are more limited and information is less complete, the population can converge to a outcome that is qualitatively different than that with global interactions and complete information.

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Kim, Jongwan, DongJin Lee, Byunggook Na, Seongsik Park, Jeonghee Jo und Sungroh Yoon. „Notice of Retraction: E2V-SDE: From Asynchronous Events to Fast and Continuous Video Reconstruction via Neural Stochastic Differential Equations“. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2022. http://dx.doi.org/10.1109/cvpr52688.2022.01319.

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Primeau, Louis, Amirali Amirsoleimani und Roman Genov. „SDEX: Monte Carlo Simulation of Stochastic Differential Equations on Memristor Crossbars“. In 2022 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2022. http://dx.doi.org/10.1109/iscas48785.2022.9937861.

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Wu, Jinglai, Yunqing Zhang, Pengfei Chen und Liping Chen. „Numerical Solution of Stochastic Differential Equations with Application to Vehicle Handling“. In SAE 2010 World Congress & Exhibition. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2010. http://dx.doi.org/10.4271/2010-01-0912.

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Wang, Yan. „Accelerating Stochastic Dynamics Simulation With Continuous-Time Quantum Walks“. In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59420.

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Stochastic diffusion is a general phenomenon observed in various national and engineering systems. It is typically modeled by either stochastic differential equation (SDE) or Fokker-Planck equation (FPE), which are equivalent approaches. Path integral is an accurate and effective method to solve FPEs. Yet, computational efficiency is the common challenge for path integral and other numerical methods, include time and space complexities. Previously, one-dimensional continuous-time quantum walk was used to simulate diffusion. By combining quantum diffusion and random diffusion, the new approach can accelerate the simulation with longer time steps than those in path integral. It was demonstrated that simulation can be dozens or even hundreds of times faster. In this paper, a new generic quantum operator is proposed to simulate drift-diffusion processes in high-dimensional space, which combines quantum walks on graphs with traditional path integral approaches. Probability amplitudes are computed efficiently by spectral analysis. The efficiency of the new method is demonstrated with stochastic resonance problems.

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Berichte der Organisationen zum Thema "Stochastic Differential Equations (SDE)"

Christensen, S. K., und G. Kallianpur. Stochastic Differential Equations for Neuronal Behavior. Fort Belvoir, VA: Defense Technical Information Center, Juni 1985. http://dx.doi.org/10.21236/ada159099.

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Dalang, Robert C., und N. Frangos. Stochastic Hyperbolic and Parabolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, Juli 1994. http://dx.doi.org/10.21236/ada290372.

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Jiang, Bo, Roger Brockett, Weibo Gong und Don Towsley. Stochastic Differential Equations for Power Law Behaviors. Fort Belvoir, VA: Defense Technical Information Center, Januar 2012. http://dx.doi.org/10.21236/ada577839.

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Sharp, D. H., S. Habib und M. B. Mineev. Numerical Methods for Stochastic Partial Differential Equations. Office of Scientific and Technical Information (OSTI), Juli 1999. http://dx.doi.org/10.2172/759177.

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Jones, Richard H. Fitting Stochastic Partial Differential Equations to Spatial Data. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada279870.

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Garrison, J. C. Stochastic differential equations and numerical simulation for pedestrians. Office of Scientific and Technical Information (OSTI), Juli 1993. http://dx.doi.org/10.2172/10184120.

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Xiu, Dongbin, und George E. Karniadakis. The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, Januar 2003. http://dx.doi.org/10.21236/ada460654.

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Chow, Pao-Liu, und Jose-Luis Menaldi. Stochastic Partial Differential Equations in Physical and Systems Sciences. Fort Belvoir, VA: Defense Technical Information Center, November 1986. http://dx.doi.org/10.21236/ada175400.

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Budhiraja, Amarjit, Paul Dupuis und Arnab Ganguly. Moderate Deviation Principles for Stochastic Differential Equations with Jumps. Fort Belvoir, VA: Defense Technical Information Center, Januar 2014. http://dx.doi.org/10.21236/ada616930.

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Webster, Clayton G., Guannan Zhang und Max D. Gunzburger. An adaptive wavelet stochastic collocation method for irregular solutions of stochastic partial differential equations. Office of Scientific and Technical Information (OSTI), Oktober 2012. http://dx.doi.org/10.2172/1081925.

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