Open Access
May, 1983 The Advantage of Using Non-Measurable Stop Rules
Theodore P. Hill, Victor C. Pestien
Ann. Probab. 11(2): 442-450 (May, 1983). DOI: 10.1214/aop/1176993609


Comparisons are made between the expected returns using measurable and non-measurable stop rules in discrete-time stopping problems. In the independent case, a natural sufficient condition ("preservation of independence") is found for the expected return of every bounded non-measurable stopping function to be equal to that of a measurable one, and for that of every unbounded non-measurable stopping function to be arbitrarily close to that of a measurable one. For non-negative and for uniformly-bounded independent random variables, universal sharp bounds are found for the advantage of using non-measurable stopping functions over using measurable ones. Partial results for the dependent case are obtained.


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Theodore P. Hill. Victor C. Pestien. "The Advantage of Using Non-Measurable Stop Rules." Ann. Probab. 11 (2) 442 - 450, May, 1983.


Published: May, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0529.60041
MathSciNet: MR690141
Digital Object Identifier: 10.1214/aop/1176993609

Primary: 60G40
Secondary: 28A20 , 90C39

Keywords: non-measurable stopping function , Optimal stopping theory , stop rule

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 2 • May, 1983
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