Exponential stability of the exact solutions and $\theta$-EM approximations to neutral SDDEs with Markov switching

TL;DR

This paper investigates the exponential stability of exact solutions and $ heta$-EM approximations for neutral stochastic differential delay equations with Markov switching, providing conditions for stability and supporting results with an example.

Contribution

It introduces new sufficient conditions for exponential stability of both exact solutions and $ heta$-EM approximations in the context of neutral SDDEs with Markov switching.

Findings

Established conditions for $p$-th moment exponential stability.

Proved almost sure exponential stability under certain conditions.

Validated results with a supporting example.

Abstract

Exponential stability of the exact solutions as well as $\theta$-EM ($\frac{1}{2}<\theta\le 1$) approximations to neutral stochastic differential delay equations with Markov switching will be investigated in this paper. Sufficient conditions are obtained to ensure the $p$-th moment ($p\ge1$) and almost sure exponential stability of the exact solutions as well as $\theta$-EM approximations ($p=2$). An example will be presented to support our conclusions.