Stability of Exponential Euler Method for Linear Stochastic Differential Equations with Piecewise Continuous Arguments

Abstract

In this paper, exponential stability in mean square of the exponential Euler method to linear stochastic differential equation with piecewise continuous arguments (LSEPCAs) is showed. We give the exponential stability in mean square of the exact solution to linear stochastic differential equation with piecewise continuous arguments by using interval with integral end-points method and definition of logarithmic norm. The exponential Euler method to linear stochastic differential equation with piecewise continuous arguments is proved to share the same stability for any step size by property of logarithmic norm. Finally, an example is provided to illustrate our theories.