A strong law of large numbers under sublinear expectations  

作　　者：Yongsheng Song 

机构地区：[1]RCSDS,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Probability, Uncertainty and Quantitative Risk》2023年第3期333-350,共18页概率、不确定性与定量风险（英文）

基　　金：supported by National Key R&D Program of China(Grant Nos.2020YFA0712700,2018YFA0703901);NSFCs(Grant No.11871458);Key Research Program of Frontier Sciences,CAS(Grant No.QYZDBSSW-SYS017).

摘　　要：We consider a sequence of independent and identically distributed(i.i.d.)random variables{ξ_(k)}under a sublinear expectation E=sup_(P∈Θ).We first give a new proof to the fact that,under each P∈Θ,any cluster point of the empirical averages.Next,we consider sublinear expectations on a Polish space,and show that for each constantμ∈[μ,μ^(-)],there exists a probability P_(μ)∈Θsuch thatlim_(n→∞)ξ_(n)=μ,P_(μ-a.s.,(0.1))supposing thatΘis weakly compact and.Under the same conditions,we obtain a generalization of(0.1)in the product space with replaced by.Here is a Borel measurable function on,.Finally,we characterize the triviality of the tail-algebra of the i.i.d.random variables under a sublinear expectation.

关 键 词：Law of large numbers Tailσ-algebra Sublinear expectation 

分 类 号：O211.5[理学—概率论与数理统计]