Difference prophet inequalities for [0,1]-valued IID random variables with cost for observations
成果类型：
Article
署名作者：
Kösters, H
署名单位：
University of Munster
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117904000000496
发表日期：
2004
页码：
3324-3332
关键词：
摘要：
Let X-1, X-2,... be a sequence of [0, 1]-valued i.i.d. random variables, let c greater than or equal to 0 be a sampling cost for each observation and let Y-i = X-i - ic, i = 1, 2,.... For n = 1, 2,..., let M(Y-1,..., Y-n) = E(max(1 less than or equal to i) (less than or equal to n) Y-i) and V(Y-1,..., Y-n) sup(tauis an element ofC)(n) E(Y-tau), where C-n denotes the set of all stopping rules for Y-1,..., Y-n. Sharp upper bounds for the difference M(Y-1,..., Y-n) -V (Y-1,..., Y-n) are given under various restrictions on c and n.