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.
Publié le : 2005-09-14
Classification:
Random times,
progressive enlargement of filtrations,
optional stopping theorem,
martingales,
general theory of processes,
60G07,
60G40,
60G44
@article{1127395874,
author = {Nikeghbali, Ashkan and Yor, Marc},
title = {A definition and some characteristic properties of pseudo-stopping times},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 1804-1824},
language = {en},
url = {http://dml.mathdoc.fr/item/1127395874}
}
Nikeghbali, Ashkan; Yor, Marc. A definition and some characteristic properties of pseudo-stopping times. Ann. Probab., Tome 33 (2005) no. 1, pp. 1804-1824. http://gdmltest.u-ga.fr/item/1127395874/