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

作者：

Highlights：

• The SDEPCA is pth moment exponentially stable with a sufficiently small τ, then the corresponding SDE is also pth moment exponentially stable.

• The EMSDE reproduces the pth moment exponential stability of the underlying SDE with a sufficiently small step size h.

• For a sufficiently small τ, the EMSDEPCA can preserve the th moment exponential stability of EMSDE.

• For a sufficiently small step size h, the EMSDEPCA is pth moment exponentially stable, then the SDEPCA is also exponentially stable in pth moment.

摘要

•The SDEPCA is pth moment exponentially stable with a sufficiently small τ, then the corresponding SDE is also pth moment exponentially stable.•The EMSDE reproduces the pth moment exponential stability of the underlying SDE with a sufficiently small step size h.•For a sufficiently small τ, the EMSDEPCA can preserve the th moment exponential stability of EMSDE.•For a sufficiently small step size h, the EMSDEPCA is pth moment exponentially stable, then the SDEPCA is also exponentially stable in pth moment.

论文关键词：Exponential stability,Stochastic differential equations,Numerical solutions,Piecewise continuous arguments

论文评审过程：Received 20 July 2020, Revised 5 October 2020, Accepted 9 November 2020, Available online 16 February 2021, Version of Record 16 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125813