Strong Laws of Large Numbers for Sublinear Expectation under Controlled 1st Moment Condition

Strong Laws of Large Numbers for Sublinear Expectation under Controlled 1st Moment Condition??

Cheng HU1

【摘 要】Abstract This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition.For a sequence of independent random variables,the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite.By discussing the relation between sublinear expectation and Choquet expectation,for a sequence of i.i.d random variables,the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense.【期刊名称】《数学年刊B辑（英文版）》【年(卷),期】2024(039)005【总页数】14

【关键词】Keywords Sublinear expectation,Strong law of large numbers,Independence,Identical distribution,Choquet expectation2000 MR Subject Classification 60F15Manuscript received November 5,2015.RevisedSeptember 27,2016.

1School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,China.E-mail:chenghusdu@126.com

??This work was supported by the National Natural Science Foundation of China(Nos.11501325,11231005).

1 Introduction

In recent years,motivated by some problems in mathematical economics,statistics and financial mathematics,more and more researches on nonlinear expectation have appeared.People use nonlinear expectation to describe some phenomena in these fields which are difficult to be modeled exactly by classical probability theory.Choquet[5] first introduced the definition of capacity and it has been used in many fields of applied