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

	Preserving asymptotic mean-square stability of stochastic theta scheme for systems of stochastic delay differential equations
Computational Methods for Differential Equations
مقاله 5، دوره 8، شماره 3، آبان 2020، صفحه 468-479 اصل مقاله (527.69 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.32139.1502
نویسنده
Omid Farkhondeh Rouz^*
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
چکیده
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.
کلیدواژه‌ها
Stochastic delay differential equations؛ Stochastic linear theta scheme؛ Asymptotic mean-square stability

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