Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations
Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations
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DOI：
10.1016/j.cam.2014.02.033
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发表时间：
2013-01
期刊：
影响因子：
--
通讯作者：
S. Gan;A. Xiao;Desheng Wang
中科院分区：
文献类型：
--
作者：
S. Gan;A. Xiao;Desheng Wang
This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean square of the solutions for nonlinear SDDEs. The results provide a unified theoretical treatment for SDDEs with constant delay and variable delay (including bounded and unbounded variable delays). Then the stability, contractivity and asymptotic contractivity in mean square are investigated for the backward Euler method. It is shown that the backward Euler method preserves the properties of the underlying SDDEs. The main results obtained in this work are different from those of Razumikhin-type theorems. Indeed, our results hold without the necessity of constructing or finding an appropriate Lyapunov functional.
