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Martingale property of empirical processes

Sergio Albeverio, Yeneng Sun, Jiang-lun Wu Orcid Logo

Transactions of the American Mathematical Society, Volume: 359, Issue: 2, Pages: 517 - 527

Swansea University Author: Jiang-lun Wu Orcid Logo

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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...

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Published in: Transactions of the American Mathematical Society
ISSN: 0002-9947 1088-6850
Published: American Mathematical Society (AMS) 2006
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URI: https://cronfa.swan.ac.uk/Record/cronfa33059
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last_indexed 2022-06-07T02:53:38Z
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spelling 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
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title 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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score 11.013776

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