Law of Large Numbers under Choquet Expectations
With a new notion of independence of random variables, we establish the nonadditive version of weak law of large numbers (LLN) for the independent and identically distributed (IID) random variables under Choquet expectations induced by 2-alternating capacities. Moreover, we weaken the moment assumpt...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/179506 |
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| _version_ | 1850231877028282368 |
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| author | Jing Chen |
| author_facet | Jing Chen |
| author_sort | Jing Chen |
| collection | DOAJ |
| description | With a new notion of independence of random variables, we establish the nonadditive version of weak law of large numbers (LLN) for the independent and identically distributed (IID) random variables under Choquet expectations induced by 2-alternating capacities. Moreover, we weaken the moment assumptions to the first absolute moment and characterize the approximate distributions of random variables as well. Naturally, our theorem can be viewed as an extension of the classical LLN to the case where the probability is no longer additive. |
| format | Article |
| id | doaj-art-08f14661b8c44bd7828c7493b0faba79 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-08f14661b8c44bd7828c7493b0faba792025-08-20T02:03:24ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/179506179506Law of Large Numbers under Choquet ExpectationsJing Chen0School of Mathematics, Shandong University, Jinan 250100, ChinaWith a new notion of independence of random variables, we establish the nonadditive version of weak law of large numbers (LLN) for the independent and identically distributed (IID) random variables under Choquet expectations induced by 2-alternating capacities. Moreover, we weaken the moment assumptions to the first absolute moment and characterize the approximate distributions of random variables as well. Naturally, our theorem can be viewed as an extension of the classical LLN to the case where the probability is no longer additive.http://dx.doi.org/10.1155/2014/179506 |
| spellingShingle | Jing Chen Law of Large Numbers under Choquet Expectations Abstract and Applied Analysis |
| title | Law of Large Numbers under Choquet Expectations |
| title_full | Law of Large Numbers under Choquet Expectations |
| title_fullStr | Law of Large Numbers under Choquet Expectations |
| title_full_unstemmed | Law of Large Numbers under Choquet Expectations |
| title_short | Law of Large Numbers under Choquet Expectations |
| title_sort | law of large numbers under choquet expectations |
| url | http://dx.doi.org/10.1155/2014/179506 |
| work_keys_str_mv | AT jingchen lawoflargenumbersunderchoquetexpectations |