Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observations

Details Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observations Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observations

2005-03-25

arxiv.org/abs/math/0503589v1

Annals of Probability 2004, Vol. 32, No. 4, 3324-3332

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000496 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000496

Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random variables, let c\geq 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\leq i\leq n}Y_i) and V(Y_1,...,Y_n)=sup_{\tau \in C^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.

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