Invariant and ergodic measures for G-diffusion processes

Abstract

In this paper we study the problems of invariant and ergodic measures under G-expectation framework. In particular, the stochastic differential equations driven by G-Brownian motion have the unique invariant and ergodic measures. Moreover, the invariant and ergodic measures of G-SDEs are also sublinear expectations. However, the invariant measures may not coincide with ergodic measures, which is different from the classical case.

References in corpus (1)

• A probabilistic approach to large time behaviour of mild solutions of Hamilton-Jacobi-Bellman equations in infinite dimension