Journal article 728 views 82 downloads
Martingale property of empirical processes
Sergio Albeverio,
Yeneng Sun,
Jiang-lun Wu 
Transactions of the American Mathematical Society, Volume: 359, Issue: 2, Pages: 517 - 527
Swansea University Author:
Jiang-lun Wu
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DOI (Published version): 10.1090/s0002-9947-06-04055-4
Abstract
It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the as- sumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales es...
| Published in: | Transactions of the American Mathematical Society |
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| ISSN: | 0002-9947 1088-6850 |
| Published: |
American Mathematical Society (AMS)
2006
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa33059 |
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| Abstract: |
It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the as- sumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given. |
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| Keywords: |
Essential independence, finite-dimensional distributions, empirical process, exact law of large numbers, Loeb product space, Keisler’s Fubini theorem, martingale, submartingale, supermartingale. |
| College: |
Faculty of Science and Engineering |
| Issue: |
2 |
| Start Page: |
517 |
| End Page: |
527 |