University of TabrizComputational Methods for Differential Equations2345-39828320200801Preserving asymptotic mean-square stability of stochastic theta scheme for systems of stochastic delay differential equations468479992110.22034/cmde.2020.32139.1502ENOmidFarkhondeh RouzFaculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.Journal Article20190224This 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.https://cmde.tabrizu.ac.ir/article_9921_3f10a4526577f99bc18606248bc855b6.pdf