Some best possible prophet inequalities for convex functions of sums of independent variates and unordered martingale difference sequences
成果类型：
Article
署名作者：
Choi, KP; Klass, MJ
署名单位：
National University of Singapore; University of California System; University of California Berkeley; University of California System; University of California Berkeley
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1997
页码：
803-811
关键词：
摘要：
Let Phi(.) be a nondecreasing convex function on [0, infinity). We show that for any integer n greater than or equal to 1 and real a, E Phi((M-n - a)(+)) less than or equal to 2E Phi((S-n - a)(+)) - Phi(0) and E(M-n boolean OR med S-n) less than or equal to E\S-n - med S-n\. where X-1, X-2,... are any independent mean zero random variables with partial sums S-0 = 0, S-k = X-1 +...+ X-k and partial sum maxima M-n = max(0 less than or equal to k less than or equal to n) S-k. There are various instances in which these inequalities are best possible for fixed n and/or as n --> infinity. These inequalities remain valid if {X-k} is a martingale difference sequence such that E(X-k \ {X-i: i not equal k}) = 0 a.s. for each k greater than or equal to 1. Modified versions of these inequalities hold if the variates have arbitrary means but are independent.