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| Strong Laws of Large Numbers for Sublinear Expectation under Controlled 1st Moment Condition |
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Citation： |
Cheng HU.Strong Laws of Large Numbers for Sublinear Expectation under Controlled 1st Moment Condition[J].Chinese Annals of Mathematics B,2018,39(5):791~804 |
| Page view： 1614
Net amount： 1431 |
Authors： |
Cheng HU; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11501325, 11231005). |
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| 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 |
Classification： |
60F15 |
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