An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
SIAM Review, 2001 A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Euler's method for deterministic differential equations and to have at least an intuitive feel for the ...
D. Higham
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Maple for Stochastic Differential Equations [PDF]
, 2001 This paper introduces the MAPLE software package stochastic consisting of MAPLE routines for stochastic calculus and stochastic differential equations and for constructing basic numerical methods for specific stochastic differential equations, with simple examples illustrating the use of the routines.
Grüne, Lars +2 more
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Stochastic differential equations
Mathematical Proceedings of the Cambridge Philosophical Society, 1955 The work of which this paper is an account began as a study of differential equations for functions whose values are random variables of finite variance.
Peter E. Kloeden
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Mean field forward-backward stochastic differential equations [PDF]
, 2012 The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the mean field type.
Rene Carmona, F. Delarue
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The Existence of Strong Solutions for a Class of Stochastic Differential Equations
International Journal of Differential Equations, 2018 In this paper, we will consider the existence of a strong solution for stochastic differential equations with discontinuous drift coefficients. More precisely, we study a class of stochastic differential equations when the drift coefficients are an ...
Junfei Zhang
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Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations [PDF]
Journal of nonlinear science, 2017 High-dimensional partial differential equations (PDEs) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment models, or portfolio optimization models. The PDEs in such applications are
C. Beck, Weinan E, Arnulf Jentzen
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Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
Journal of Applied Mathematics, 2012 We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s ...
Li Chen, Zhen Wu, Zhiyong Yu
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Stability of Stochastic Partial Differential Equations
Axioms, 2023 In this paper, we study the stability of the stochastic parabolic differential equation with dependent coefficients. We consider the stability of an abstract Cauchy problem for the solution of certain stochastic parabolic differential equations in a ...
Allaberen Ashyralyev, Ülker Okur
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Stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential algebraic equations
Results in Applied Mathematics, 2021 In this paper, we discuss the numerical solutions to index 1 stochastic differential algebraic equations. We introduce a new class of weak second-order stochastic Runge–Kutta methods for finding the numerical approximate solutions to multi-dimensional ...
Priya Nair, Anandaraman Rathinasamy
doaj
Stability of numerical method for semi-linear stochastic pantograph differential equations
Journal of Inequalities and Applications, 2016 As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics.
Yu Zhang, Longsuo Li
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