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

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 ($p\ge 1$) 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.

18 pages

References in corpus (1)

• Mean Square Polynomial Stability of Numerical Solutions to a Class of Stochastic Differential Equations