Ergodicity for functional stochastic differential equations and applications

Abstract

In this paper, using the remote start or dissipative method, we investigate ergodicity for several kinds of functional stochastic equations including functional stochastic differential equations (SDEs) with variable delays, neutral functional SDEs, functional SDEs driven by jump processes, and semi-linear functional stochastic partial differential equations (SPDEs). Using the ergodicity derived, we then treat a couple of applications in stochastic approximation and optimization problems.