Approximate solutions of stochastic differential delay equations with Markovian switching [PDF]
, 2010 Our main aim is to develop the existence theory for the solutions to stochastic differential delay equations with Markovian switching (SDDEwMSs) and to establish the convergence theory for the Euler-Maruyama approximate solutions under the local ...
Li, Xiaoyue +4 more
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Patchwork sampling of stochastic differential equations [PDF]
Physical Review E, 2016 We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The method is based on a complete, non-overlapping partition of the state space into patches on which the stochastic ...
Kürsten, Rüdiger, Behn, Ulrich
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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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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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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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Covariance structure of parabolic stochastic partial differential equations [PDF]
, 2012 In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered.
Lang, Annika +5 more
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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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Asymptotic behaviours of stochastic differential delay equations
, 2005 Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper.
Shen, Yi +3 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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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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