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A definition and some characteristic properties of pseudo-stopping times


Nikeghbali, A; Yor, M (2005). A definition and some characteristic properties of pseudo-stopping times. The Annals of Probability, 33(5):1804-1824.

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 E(Mρ)=E(M0) 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 filtration

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 E(Mρ)=E(M0) 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 filtration

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Random times; progressive enlargement of filtrations; optional stopping theorem; martingales; general theory of processes
Language:English
Date:2005
Deposited On:29 Nov 2010 16:26
Last Modified:06 Dec 2017 20:47
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
Publisher DOI:https://doi.org/10.1214/009117905000000297
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1083.60035
http://www.ams.org/mathscinet-getitem?mr=2165580

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