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Ergodicity on Sublinear Expectation Spaces
时间  Datetime
2017-12-29 16:00 — 17:00 
地点  Venue
Large Conference Room
报告人  Speaker
赵怀忠
单位  Affiliation
英国拉夫堡大学教授
邀请人  Host
熊德文
报告摘要  Abstract

In this paper, we first develop an ergodic theory of an expectation-preserving map 
on a sublinear expectation space. Ergodicity is defined as any invariant set either 
has $0$ capacity itself or its complement has $0$ capacity. We prove, under a general 
sublinear expectation space setting, the equivalent relation between ergodicity and the 
corresponding transformation operator having simple eigenvalue $1$, and also 
with Birkhoff type strong law of large numbers if the sublinear expectation is strongly regular.
We also study the ergodicity of invariant sublinear expectation of sublinear Markovian semigroup. 
We prove that its ergodicity is equivalent to the generator of the Markovian semigroup having 
eigenvalue $0$ and the eigenvalue is simple in the space of continuous functions. As an example 
we show that $G$-Brownian motion on the unit circle has an invariant expectation and is ergodic.
Moreover, it is also proved in this case that the invariant expectation is strongly regular and the
canonical stationary process has no mean-uncertainty under the invariant expectation. 
This is a joint work with Chunrong Feng.