Invariant and ergodic measures for G-diffusion processes

TL;DR

This paper investigates invariant and ergodic measures for G-diffusion processes, revealing unique measures under G-expectation and highlighting differences from classical cases.

Contribution

It establishes the existence and uniqueness of invariant and ergodic measures for G-SDEs driven by G-Brownian motion within the G-expectation framework.

Findings

Unique invariant measures for G-SDEs

Invariant and ergodic measures are sublinear expectations

Invariant measures may differ from ergodic measures

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.