%0 Journal Article
%T Preserving asymptotic mean-square stability of stochastic theta scheme for systems of stochastic delay differential equations
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Farkhondeh Rouz, Omid
%D 2020
%\ 08/01/2020
%V 8
%N 3
%P 468-479
%! Preserving asymptotic mean-square stability of stochastic theta scheme for systems of stochastic delay differential equations
%K Stochastic delay differential equations
%K Stochastic linear theta scheme
%K Asymptotic mean-square stability
%R 10.22034/cmde.2020.32139.1502
%X 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.
%U https://cmde.tabrizu.ac.ir/article_9921_3f10a4526577f99bc18606248bc855b6.pdf