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

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.

Keywords

Sublinear expectation / Strong law of large numbers / Independence / Identical distribution / Choquet expectation

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