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, W. E, Arnulf Jentzen
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Marcus Stochastic Differential Equations: Representation of Probability Density
MathematicsMarcus stochastic delay differential equations are often used to model stochastic dynamical systems with memory in science and engineering. It is challenging to study the existence, uniqueness, and probability density of Marcus stochastic delay ...
Fang Yang, Chen Fang, Xu Sun
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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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Stochastic Differential Equations
Journal of Multivariate Analysis, 1974 AbstractWhen a system is acted upon by exterior disturbances, its time-development can often be described by a system of ordinary differential equations, provided that the disturbances are smooth functions. But for sound reasons physicists and engineers usually want the theory to apply when the noises belong to a larger class, including for example ...
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Functional Methods in Stochastic Systems
, 2012 Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put forward ...
A.N. Vasiliev +9 more
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Averaged Systems of Stochastic Differential Equations with Lévy Noise and Fractional Brownian Motion
Fractal and FractionalIn some problems, partial differential equations are reduced to ordinary differential equations. In special cases, when incorporating randomness, equations can be reduced to systems of stochastic differential Equations (SDEs).
Tayeb Blouhi +6 more
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Periodic Averaging Principle for Neutral Stochastic Delay Differential Equations with Impulses
Complexity, 2020 In this paper, we study the periodic averaging principle for neutral stochastic delay differential equations with impulses under non-Lipschitz condition.
Peiguang Wang, Yan Xu
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Abstract and Applied Analysis, 2014 Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before.
Qingfeng Zhu, Yufeng Shi
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Numerical Methods for Stochastic Differential Equations
, 2004 Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability.
C. W. Gardiner +5 more
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