Journal article 812 views 99 downloads
Martingale property of empirical processes
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 |
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American Mathematical Society (AMS)
2006
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URI: | https://cronfa.swan.ac.uk/Record/cronfa33059 |
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2022-06-06T15:36:47.2632669 v2 33059 2017-04-25 Martingale property of empirical processes dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2017-04-25 SMA 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. Journal Article Transactions of the American Mathematical Society 359 2 517 527 American Mathematical Society (AMS) 0002-9947 1088-6850 Essential independence, finite-dimensional distributions, empirical process, exact law of large numbers, Loeb product space, Keisler’s Fubini theorem, martingale, submartingale, supermartingale. 19 9 2006 2006-09-19 10.1090/s0002-9947-06-04055-4 http://dx.doi.org/10.1090/s0002-9947-06-04055-4 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University Other 2022-06-06T15:36:47.2632669 2017-04-25T16:17:23.7926522 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Sergio Albeverio 1 Yeneng Sun 2 Jiang-lun Wu 0000-0003-4568-7013 3 0033059-25042017161826.pdf AlSunWuTransAMS2007-S0002-9947-06-04055-4.pdf 2017-04-25T16:18:26.0230000 Output 207080 application/pdf Accepted Manuscript true 2017-04-25T00:00:00.0000000 true eng |
title |
Martingale property of empirical processes |
spellingShingle |
Martingale property of empirical processes Jiang-lun Wu |
title_short |
Martingale property of empirical processes |
title_full |
Martingale property of empirical processes |
title_fullStr |
Martingale property of empirical processes |
title_full_unstemmed |
Martingale property of empirical processes |
title_sort |
Martingale property of empirical processes |
author_id_str_mv |
dbd67e30d59b0f32592b15b5705af885 |
author_id_fullname_str_mv |
dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu |
author |
Jiang-lun Wu |
author2 |
Sergio Albeverio Yeneng Sun Jiang-lun Wu |
format |
Journal article |
container_title |
Transactions of the American Mathematical Society |
container_volume |
359 |
container_issue |
2 |
container_start_page |
517 |
publishDate |
2006 |
institution |
Swansea University |
issn |
0002-9947 1088-6850 |
doi_str_mv |
10.1090/s0002-9947-06-04055-4 |
publisher |
American Mathematical Society (AMS) |
college_str |
Faculty of Science and Engineering |
hierarchytype |
|
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facultyofscienceandengineering |
hierarchy_top_title |
Faculty of Science and Engineering |
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
department_str |
School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
url |
http://dx.doi.org/10.1090/s0002-9947-06-04055-4 |
document_store_str |
1 |
active_str |
0 |
description |
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. |
published_date |
2006-09-19T03:40:39Z |
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1763751850149937152 |
score |
11.021648 |