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 |
Appears in Collections: | Staff Publications |
Show full item record
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.