Preserving asymptotic mean-square stability of stochastic theta scheme for systems of stochastic delay differential equations

Document Type : Research Paper

Author

Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.

Abstract

This article examines asymptotic mean-square stability analysis of stochastic linear theta (SLT) scheme for n-dimensional stochastic delay differential equations (SDDEs). We impose some conditions on drift and diffusion terms, which admit that the diffusion coefficient can be highly nonlinear and does not necessarily satisfy a linear growth or global Lipschitz condition. We prove that the proposed scheme is asymptotically mean square stable if the employed stepsize is smaller than a given and easily computable upper bound. In particular, based on our investigation in the case θ ∈[ 1/2 , 1], the stepsize is arbitrary. Eventually, numerical examples are given to demonstrate the effectiveness of our work.

Keywords

Computational Methods for Differential Equations
Volume 8, Issue 3
August 2020
Pages 468-479

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History

  • Receive Date: 24 February 2019
  • Revise Date: 14 May 2019
  • Accept Date: 14 May 2019

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