Recommended Citation
Published in Proceedings of the American Mathematical Society, Volume 83, Issue 3, November 1, 1981, pages 582-585. Copyright © 1981 The American Mathematical Society. The definitive version is available at http://dx.doi.org/10.1090/S0002-9939-1981-0627697-3.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
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.
Disciplines
Mathematics
URL: http://digitalcommons.calpoly.edu/rgp_rsr/65