Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9947-06-04055-4
Title: Martingale property of empirical processes
Authors: Albeverio, S.
Sun, Y. 
Wu, J.-L.
Keywords: Empirical process
Essential independence
Exact law of large numbers
Finite-dimensional distributions
Keisler's Fubini theorem
Loeb product space
Martingale
Submartingale
Supermartingale
Issue Date: Feb-2007
Citation: Albeverio, S., Sun, Y., Wu, J.-L. (2007-02). Martingale property of empirical processes. Transactions of the American Mathematical Society 359 (2) : 517-527. ScholarBank@NUS Repository. https://doi.org/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 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. © 2006 American Mathematical Society.
Source Title: Transactions of the American Mathematical Society
URI: http://scholarbank.nus.edu.sg/handle/10635/114167
ISSN: 00029947
DOI: 10.1090/S0002-9947-06-04055-4
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