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April, 1973 Which Functions of Stopping Times are Stopping Times?
Lester E. Dubins
Ann. Probab. 1(2): 313-316 (April, 1973). DOI: 10.1214/aop/1176996983

Abstract

Some functions of stopping times are necessarily stopping times, but others need not be. For example, the sum $\tau_1 + \tau_2$ of two stopping times is, while for stochastic processes in continuous time, the product $\tau_1 \cdot \tau_2$ need not be. Determined here for each positive integer $n$ are those functions $\phi$ for which $\phi(\tau)$ is a stopping time for all $n$-triples of stopping times $\tau = \tau_1, \cdots, \tau_n$.

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Lester E. Dubins. "Which Functions of Stopping Times are Stopping Times?." Ann. Probab. 1 (2) 313 - 316, April, 1973. https://doi.org/10.1214/aop/1176996983

Information

Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0273.60026
MathSciNet: MR350843
Digital Object Identifier: 10.1214/aop/1176996983

Subjects:
Primary: 60G40
Secondary: 60J25

Keywords: Stochastic processes , stop rules , stopping times

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 2 • April, 1973
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