报告题目 (Title)：The Law of Large Numbers and Ergodicity under Sublinear Expectations（次线性期望下的大数定律和遍历性）

报告人 (Speaker)：宋永生 研究员（中科院数学与系统科学研究院）

报告时间 (Time)：2023年3月14日 (周二) 14:00-17:00

报告地点 (Place)：腾讯会议（会议号：140-499-720 无密码）

邀请人(Inviter)：阳芬芬

主办部门：理学院数学系

报告摘要：Peng (2007) proved the (weak) law of large numbers (LLN) under sublinear expectations with convergence in distribution. After that, many literatures are devoted to studying the strong version of LLN, as well as ergodicity under sublinear expectations, in the sense of almost surely convergence. Most of these results are discussed under the continuity assumption of the capacities.

In this talk, we first give a characterization of the continuous capacities, based on which we improve the ergodicity results in Cerreia-Vioglio, et al (2016). This characterization also shows that the continuity of the capacities is a very strong assumption for LLN and ergodicity under sublinear expectations. To get rid of this assumption, we give a version of strong LLN under regular sublinear expectations defined on a Polish space, which shows that any constant u in the mean interval [a, b] can be considered as a limit of the empirical averages.