Title

Ratio Comparisons of Supremum and Stop Rule Expectations

Author Info

Theodore P. Hill, Georgia Institute of Technology - Main CampusFollow
Robert P. Kertz, Georgia Institute of Technology - Main Campus

Recommended Citation

Postprint version. Published in Probability Theory and Related Fields, Volume 56, Issue 2, June 1, 1981, pages 283-285.

Copyright © 1981 Springer.

NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.

The definitive version is available at https://doi.org/10.1007/BF00535745.

Abstract

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

Disciplines

Mathematics