Preserving asymptotic mean-square stability of stochastic theta scheme for systems of stochastic delay differential equations
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_CMDE-8-3_005
تاریخ نمایه سازی: 15 بهمن 1401
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 ∈[ ۱/۲ , ۱], the stepsize is arbitrary. Eventually, numerical examples are given to demonstrate the effectiveness of our work.
Keywords:
Stochastic delay differential equations , Stochastic linear theta scheme , Asymptotic mean-square stability
Authors
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Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.