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arXiv · 2001.05203

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

Minghui Song·Yidan Geng·Mingzhu Liu
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Abstract

In this paper, we consider the equivalence of the $p$th 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 $p$th moment exponentially stable, then any of them is $p$th moment exponentially stable for a sufficiently small step size $h$ and $\tau$ under the global Lipschitz assumption on the drift and diffusion coefficients

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Minghui Song, Yidan Geng, Mingzhu Liu. 2020-01-15. Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods. https://arxiv.org/abs/2001.05203

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