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- Title
Preserving asymptotic mean-square stability of stochastic theta scheme for systems of stochastic delay differential equations.
- Authors
Rouz, Omid Farkhondeh
- 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.
- Subjects
MEAN square algorithms; THETA functions; LIPSCHITZ spaces; NUMERICAL analysis; MATHEMATICAL models of diffusion
- Publication
Computational Methods for Differential Equations, 2020, Vol 8, Issue 3, p468
- ISSN
2345-3982
- Publication type
Article
- DOI
10.22034/cmde.2020.32139.1502