论文标题
随机微分方程和随机微分方程之间的稳定性等效性具有分段连续参数和相应的Euler-Maruyama方法
Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods
论文作者
论文摘要
在本文中，我们考虑了随机微分方程（SDES），带有分段连续参数（SDEPCAS）的随机微分方程（SDEPCAS）和相应的Euler-Maruyama方法EMSDES和EMSDEPCAS的$ P $ TH矩指数稳定性的等效性。我们表明，如果SDEPCA，SDE，EMSDES和EMSDEPCAS之一是$ p $ th时刻，那么在$ p $ p $ th时刻是$ p $ th时刻，对于足够小的步长$ h $和$ h $和$τ$，在全球liplipschitz上的漂移系数和扩散系数上，
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 $τ$ under the global Lipschitz assumption on the drift and diffusion coefficients
