Relationship between stochastic inequalities and some classical mathematical inequalities
The notions of association and dependence of random variables, rearrangements, and heterogeneity via majorization ordering have proven to be most useful for deriving stochastic inequalities. In this survey article we first show that these notions are closely related to three basic inequalities in cl...
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| Format: | Article |
| Language: | English |
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SpringerOpen
1997-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1025583497000064 |
| _version_ | 1818363629213319168 |
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| author | Y. L. Tong |
| author_facet | Y. L. Tong |
| author_sort | Y. L. Tong |
| collection | DOAJ |
| description | The notions of association and dependence of random variables, rearrangements, and heterogeneity via majorization ordering have proven to be most useful for deriving stochastic inequalities. In this survey article we first show that these notions are closely related to three basic inequalities in classical mathematical analysis: Chebyshev’s inequality, the Hardy-Littlewood-Pólya rearrangement inequality and Schur functions. We then provide a brief review of some of the recent results in this area. An overall objective is to illustrate that classical mathematical inequalities of this type play a central role in the developments of stochastic inequalities. |
| first_indexed | 2024-12-13T21:51:31Z |
| format | Article |
| id | doaj.art-d2c572c5c4824ddfa18a153ff283bc69 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-13T21:51:31Z |
| publishDate | 1997-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d2c572c5c4824ddfa18a153ff283bc692022-12-21T23:30:16ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1997-01-0111859810.1155/S1025583497000064Relationship between stochastic inequalities and some classical mathematical inequalitiesY. L. TongThe notions of association and dependence of random variables, rearrangements, and heterogeneity via majorization ordering have proven to be most useful for deriving stochastic inequalities. In this survey article we first show that these notions are closely related to three basic inequalities in classical mathematical analysis: Chebyshev’s inequality, the Hardy-Littlewood-Pólya rearrangement inequality and Schur functions. We then provide a brief review of some of the recent results in this area. An overall objective is to illustrate that classical mathematical inequalities of this type play a central role in the developments of stochastic inequalities.http://dx.doi.org/10.1155/S1025583497000064stochastic inequalities; association; rearrangements; majorization and Schur functions. |
| spellingShingle | Y. L. Tong Relationship between stochastic inequalities and some classical mathematical inequalities Journal of Inequalities and Applications stochastic inequalities; association; rearrangements; majorization and Schur functions. |
| title | Relationship between stochastic inequalities and some classical mathematical inequalities |
| title_full | Relationship between stochastic inequalities and some classical mathematical inequalities |
| title_fullStr | Relationship between stochastic inequalities and some classical mathematical inequalities |
| title_full_unstemmed | Relationship between stochastic inequalities and some classical mathematical inequalities |
| title_short | Relationship between stochastic inequalities and some classical mathematical inequalities |
| title_sort | relationship between stochastic inequalities and some classical mathematical inequalities |
| topic | stochastic inequalities; association; rearrangements; majorization and Schur functions. |
| url | http://dx.doi.org/10.1155/S1025583497000064 |
| work_keys_str_mv | AT yltong relationshipbetweenstochasticinequalitiesandsomeclassicalmathematicalinequalities |