Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Martingale property of empirical processes

Authors: Sergio Albeverio, Yeneng Sun and Jiang-Lun Wu
Journal: Trans. Amer. Math. Soc. 359 (2007), 517-527
MSC (2000): Primary 60G42, 60G44; Secondary 03H05, 28E05, 60F15
Published electronically: September 19, 2006
MathSciNet review: 2255184
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 60G42, 60G44, 03H05, 28E05, 60F15

Retrieve articles in all journals with MSC (2000): 60G42, 60G44, 03H05, 28E05, 60F15

Additional Information

Sergio Albeverio
Affiliation: Institut für Angewandte Mathematik der Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany

Yeneng Sun
Affiliation: Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore

Jiang-Lun Wu
Affiliation: Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom

PII: S 0002-9947(06)04055-4
Keywords: Essential independence, finite-dimensional distributions, empirical process, exact law of large numbers, Loeb product space, Keisler's Fubini theorem, martingale, submartingale, supermartingale.
Received by editor(s): September 16, 2004
Published electronically: September 19, 2006
Article copyright: © Copyright 2006 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia