A Definition and Some Characteristic Properties of Pseudo-Stopping Times

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 EMρ= EM0for every bounded martingale M. The aim of this paper is to characterize such random times, which we call pseudo-s...

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Veröffentlicht in:	The Annals of probability 2005-09, Vol.33 (5), p.1804-1824
Hauptverfasser:	Nikeghbali, Ashkan, Yor, Marc
Format:	Artikel
Sprache:	eng
Schlagworte:	60G07 60G40 60G44 Brownian motion Exact sciences and technology general theory of processes Logical givens Martingales Mathematical models Mathematics optional stopping theorem Probabilities Probability Probability and statistics Probability theory and stochastic processes progressive enlargement of filtrations Random times Random variables Random walk Sciences and techniques of general use Stochastic processes Stopping distances Temporal logic Theory Uniform laws
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Zusammenfassung:	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 EMρ= EM0for 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.
ISSN:	0091-1798 2168-894X
DOI:	10.1214/009117905000000297