Open Access
Translator Disclaimer
September 2005 A definition and some characteristic properties of pseudo-stopping times
Ashkan Nikeghbali, Marc Yor
Ann. Probab. 33(5): 1804-1824 (September 2005). DOI: 10.1214/009117905000000297

Abstract

Recently, Williams [Bull. London Math. Soc. 34 (2002) 610–612] gave an explicit example of a random time ρ associated with Brownian motion such that ρ is not a stopping time but $\mathbb{E}M_{\rho }=\mathbb{E}M_{0}$ for every bounded martingale M. The aim of this paper is to characterize such random times, which we call pseudo-stopping times, and to construct further examples, using techniques of progressive enlargements of filtrations.

Citation

Download Citation

Ashkan Nikeghbali. Marc Yor. "A definition and some characteristic properties of pseudo-stopping times." Ann. Probab. 33 (5) 1804 - 1824, September 2005. https://doi.org/10.1214/009117905000000297

Information

Published: September 2005
First available in Project Euclid: 22 September 2005

zbMATH: 1083.60035
MathSciNet: MR2165580
Digital Object Identifier: 10.1214/009117905000000297

Subjects:
Primary: 60G07 , 60G40 , 60G44

Keywords: general theory of processes , Martingales , optional stopping theorem , progressive enlargement of filtrations , Random times

Rights: Copyright © 2005 Institute of Mathematical Statistics

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.33 • No. 5 • September 2005
Back to Top