T-Stability of the Euler Method for Impulsive Stochastic Differential Equations Driven by Fractional Brownian Motion

Abstract

Due to the fact that a fractional Brownian motion (fBm) with the Hurst parameter $H\in (0,1/2)\cup (1/2,1)$ is neither a semimartingale nor a Markov process, relatively little is studied about the T-stability for impulsive stochastic differential equations (ISDEs) with fBm. Here, for such linear equations with $H\in (1/3,1/2)$,
by means of the average stability function,
sufficient conditions of the T-stability are presented to their numerical solutions which are established from the Euler-Maruyama method with variable step-size. Moreover, some numerical
examples are presented to support the theoretical results.