Ergodicity for regime-switching neutral stochastic functional differential equations with infinite delay

Abstract

This work focuses on a class of regime-switching neutral stochastic functional differential equations (RNSFDEs) with infinite delay, in which the switching component can possess finite or countably infinite many states. To ensure the well-posedness of the underlying process, we first investigate the well-posedness for NSFDEs without Markovian switching under dissipativity conditions, and obtain the desired result by Skorohod's representation. By utilizing the moment estimate of exponential functionals of the switching component, we derive the exponential ergodicity in Wasserstein distance for RNSFDEs with a finite state space using the coupling method. To address the difficulty posed by the infinite state space, we obtain the same exponential ergodicity by applying the finite partition method along with Lyapunov functions and M-matrix theory.