Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observations
Abstract
Description
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_{τ\in C^n}E(Y_τ), 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.
Published at http://dx.doi.org/10.1214/009117904000000496 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Published at http://dx.doi.org/10.1214/009117904000000496 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)