Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations
Abstract and Applied Analysis, 2014 Our effort is to develop a criterion on almost surely exponential stability of numerical solution to stochastic pantograph differential equations, with the help of the discrete semimartingale convergence theorem and the technique used in stable analysis ...
Shaobo Zhou
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Investigation of high order stochastic differential equations using averaging method
Vietnam Journal of Mechanics, 2007 The averaging method is a useful tool for investigating both deterministic and stochastic quasilinear system. In the stochastic problems, however, the method has often been developed only for mechanical systems subjected to white noise excitations.In the
Nguyen Dong Anh, Ngo Thi Hong Hue
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A Semidiscrete Galerkin Scheme for Backward Stochastic Parabolic Differential Equations [PDF]
, 2022 Yanqing Wang
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Spectral functions related to some fractional stochastic differential equations [PDF]
, 2022 Mirko D’Ovidio +2 more
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AIP Advances, 2023 Stochastic methods significantly solve stochastic differential equations such as stochastic equations with a delay, stochastic fractional and fractal equations, stochastic partial differential equations, and many more.
Wafa F. Alfwzan +5 more
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Stochastic Stability of Differential Equations in Abstract Spaces
, 2019 We begin by recalling some basic definitions and results, especially those from functional analysis, partial differential equations (PDEs), probability, and stability theories.
Kai Liu
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Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation
Abstract and Applied Analysis, 2011 This paper investigates the existence and uniqueness of mild solutions to the general nonlinear stochastic impulsive differential equations. By using Schaefer's fixed theorem and stochastic analysis technique, we propose sufficient conditions on ...
L. J. Shen, J. T. Sun
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Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations
Mathematics, 2016 Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed.
Yanmei Liu, Monzorul Khan, Yubin Yan
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Stochastic Discontinuous Galerkin Methods (SDGM) based on fluctuation-dissipation balance
Results in Applied Mathematics, 2019 We introduce a general framework for approximating parabolic Stochastic Partial Differential Equations (SPDEs) based on fluctuation-dissipation balance. Using this approach we formulate Stochastic Discontinuous Galerkin Methods (SDGM).
W. Pazner, N. Trask, P.J. Atzberger
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A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients
Journal of Applied Mathematics, 2004 We attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward ...
Omid. S. Fard, Ali V. Kamyad
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