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Additive Comparisons of Stop Rule and Supremum Expectations of Uniformly Bounded Independent Random Variables
Proceedings of the American Mathematical Society
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
  • Robert P. Kertz, Georgia Institute of Technology - Main Campus
Publication Date
11-1-1981
Abstract

Let XI, X2, . . . be independent random variables taking values in [a, b], and let T denote the stop rules for X1, X2, Then E(supn>1 Xn) - sup{ EXt t ≡ T} < (1/4)(b - a), and this bound is best possible. Probabilistically, this says that if a prophet (player with complete foresight) makes a side payment of (b - a)/8 to a gambler (player using nonanticipating stop rules), the game becomes at least fair for the gambler.

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Citation Information
Theodore P. Hill and Robert P. Kertz. "Additive Comparisons of Stop Rule and Supremum Expectations of Uniformly Bounded Independent Random Variables" Proceedings of the American Mathematical Society Vol. 83 Iss. 3 (1981) p. 582 - 585
Available at: http://works.bepress.com/tphill/42/