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Article
The Advantage of Using Non-Measurable Stop Rules
The Annals of Probability
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
  • Victor C. Prestien, Georgia Institute of Technology - Main Campus
Publication Date
5-1-1983
Abstract
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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Citation Information
Theodore P. Hill and Victor C. Prestien. "The Advantage of Using Non-Measurable Stop Rules" The Annals of Probability Vol. 11 Iss. 2 (1983) p. 442 - 450
Available at: http://works.bepress.com/tphill/6/