A definition and some characteristic properties of pseudo-stopping times

A definition and some characteristic properties of pseudo-stopping times

Ashkan Nikeghbali and Marc Yor

Source: Ann. Probab. Volume 33, Number 5 (2005), 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 $\mathbb{E}M_{\rho }=\mathbb{E}M_{0}$ 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.

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Primary Subjects: 60G07, 60G40, 60G44

Keywords: Random times; progressive enlargement of filtrations; optional stopping theorem; martingales; general theory of processes

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Permanent link to this document: http://projecteuclid.org/euclid.aop/1127395874
Digital Object Identifier: doi:10.1214/009117905000000297
Mathematical Reviews number (MathSciNet): MR2165580
Zentralblatt MATH identifier: 1083.60035

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