Abstract

Suppose X1,X2,...,Xn are independent non-negative random variables with finite positive expectations. Let Tn denote the stop rules for X1,...,Xn. The main result of this paper is that E(max{X1,...,Xn }) sup{EXt t ε Tn }. The proof given is constructive, and sharpens the corresponding weak inequalities of Krengel and Sucheston and of Garling.

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URL: http://digitalcommons.calpoly.edu/rgp_rsr/63