Doob, Ignatov and optional skipping.
type: Item
instance of: scholarly article
title: Doob, Ignatov and optional skipping.
zbMATH Open document ID: 1040.60034
author: Gordon Simons
author: Yi-Ching Yao
author: L. Yang
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: Let \(\xi_1,\xi_2,\dots\) be an i.i.d. sequence of random variables, taking values in a measurable space with common distribution \(F\). The authors describe a general set of conditions on a sequence of stopping times \(\tau_1,\tau_2,\dots\), not depending on \(F\), which guarantee that \(\xi_{\tau_1},\xi_{\tau_2}.\dots\) be i.i.d. with common distribution \(F\). This work is motivated by theorems of \textit{J. L. Doob} [Ann. Math. (2) 37, 363--367 (1936; Zbl 0013.40802)] and \textit{Z. Ignatov} [God. Sofij. Univ., Fak. Mat. Mekh. 71 (1976/1977), Part II, 79--94 (1986; Zbl 0619.60052)]. The authors unify and extend aspects of both.
reviewed by: Yoshio Ohtsubo
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 1906105
zbMATH Keywords: optimal skipping
zbMATH Keywords: Ignatov's theorem
zbMATH Keywords: indexical stopping time
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1039548377
OpenAlex ID: W2104827057
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DOI: 10.1214/AOP/1039548377
description: scientific article; zbMATH DE number 1906105