In my talk, I will first talk an ergodic theory of an expectation-preserving map on a sublinear expectation space. We also study the ergodicity of invariant sublinear expectation of sublinear Markovian semigroup. As an example we show that G-Brownian motion on the unit circle has an invariant expectation and is ergodic. Moreover, I will discuss the ergodic theory of invariant capacity. This is a joint work with Huaizhong Zhao. |