Almost sure exponential stability of hybrid stochastic functional differential equations (Q1682117)

This paper is concerned with almost sure exponential stability of an \(n\)-dimensional nonlinear hybrid stochastic functional differential equation (SFDE) modelled by a Markov chain. Under Lipschitz condition, the authors show that if the corresponding hybrid SDE is almost surely exponentially stable, then there exists a positive number \(\tau^*\) such that the SFDE is also almost surely exponentially stable if \(\tau<\tau^*\). They also describe a method to determine \(\tau^*\) which can be computed numerically. Several special classes of hybrid SFDEs are discussed.