Back to Search
Start Over
The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations.
- Source :
-
Acta Mathematica Sinica . Dec2023, Vol. 39 Issue 12, p2283-2315. 33p. - Publication Year :
- 2023
-
Abstract
- In this paper, by establishing a Borel–Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random variables on ℝ∞ under a probability, we give the sufficient and necessary conditions of the strong law of large numbers for independent and identically distributed random variables under the sub-linear expectation, and the sufficient and necessary conditions for the convergence of an infinite series of independent random variables, without the assumption on the continuity of the capacities. A purely probabilistic proof of a weak law of large numbers is also given. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 39
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 174096182
- Full Text :
- https://doi.org/10.1007/s10114-023-1103-4