»ã±¨±êÌâ (Title)£ºThe Law of Large Numbers and Ergodicity under Sublinear Expectations£¨´ÎÏßÐÔ½øչϵĴóÊý¶¨ÂɺͱéÀúÐÔ£©

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»ã±¨¹¦·ò (Time)£º2023Äê3ÔÂ14ÈÕ (Öܶþ) 14:00-17:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飨»áÒéºÅ£º140-499-720 ÎÞÃÜÂ룩

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»ã±¨ÌáÒª£ºPeng (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.