Doob, Ignatov and Optional Skipping

A general set of distribution-free conditions is described under which an i.i.d. sequence of random variables is preserved under optional skipping. This work is motivated by theorems of J. L. Doob [Ann. of Math. 37 (1936) 363-367] and Z. Ignatov [Annuaire Univ. Sofia Fac. Math. Méch. 71 (1977) 79-94...

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Veröffentlicht in:	The Annals of probability 2002-10, Vol.30 (4), p.1933-1958
Hauptverfasser:	Simons, Gordon, Yao, Yi-Ching, Yang, Lijian
Format:	Artikel
Sprache:	eng
Schlagworte:	28D05 60G40 Backward induction Definiteness disentangled stopping times Distribution theory Exact sciences and technology Ignatov's theorem indexical stopping times Indexicality Induction assumption k-records Logical givens Mathematical analysis Mathematical theorems Mathematics Measure and integration optional skipping Probability and statistics Probability theory and stochastic processes Random variables records Sciences and techniques of general use Stochastic processes Stopping distances Truncation
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Beschreibung
Zusammenfassung:	A general set of distribution-free conditions is described under which an i.i.d. sequence of random variables is preserved under optional skipping. This work is motivated by theorems of J. L. Doob [Ann. of Math. 37 (1936) 363-367] and Z. Ignatov [Annuaire Univ. Sofia Fac. Math. Méch. 71 (1977) 79-94], unifying and extending aspects of both.
ISSN:	0091-1798 2168-894X
DOI:	10.1214/aop/1039548377