Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods

Minghui Song, Yidan Geng and Mingzhu Liu

Applied Mathematics and Computation, 2021, vol. 400, issue C

Abstract: In this paper, we consider the equivalence of the pth moment exponential stability for stochastic differential equations (SDEs), stochastic differential equations with piecewise continuous arguments (SDEPCAs) and the corresponding Euler-Maruyama methods EMSDEs and EMSDEPCAs. We show that if one of the SDEPCAs, SDEs, EMSDEs and EMSDEPCAs is pth moment exponentially stable, then any of them is pth moment exponentially stable for a sufficiently small step size h and τ under the global Lipschitz assumption on the drift and diffusion coefficients.

Keywords: Exponential stability; Stochastic differential equations; Numerical solutions; Piecewise continuous arguments (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300320307669

DOI: 10.1016/j.amc.2020.125813

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