A definition and some characteristic properties of pseudo-stopping times

2004/06/23 by Ashkan Nikeghbali, Marc Yor, Nikeghbali, Ashkan +1 · 1 citation
Business, Management and Accounting · Computer Science · Mathematics · #60G07 #60G40 #60G44 #Advanced Queuing Theory Analysis #FOS: Mathematics #Petri Nets in System Modeling #Probability (math.PR) #math.PR #msc:60G07 #msc:60G40 #msc:60G44

paper · pdf · doi:10.48550/arxiv.math/0406459

30 pages; to appear in Annals of Probability

openalex publication_date 2004/06/23 · arxiv created 2004/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, D. Williams \citewilliams gave an explicit example of a random time ρ associated with Brownian motion such that ρ is not a stopping time but 𝔼M_ρ=𝔼M₀ for every bounded martingale M. The aim of this paper is to give some characterizations for 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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