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October 2004 Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observations
Holger Kösters
Ann. Probab. 32(4): 3324-3332 (October 2004). DOI: 10.1214/009117904000000496

Abstract

Let X1,X2,… be a sequence of [0,1]-valued i.i.d. random variables, let c≥0 be a sampling cost for each observation and let Yi=Xiic, i=1,2,…. For n=1,2,…, let M(Y1,…,Yn)=E(max 1≤inYi) and V(Y1,…,Yn)=sup τ∈CnE(Yτ), where Cn denotes the set of all stopping rules for Y1,…,Yn. Sharp upper bounds for the difference M(Y1,…,Yn)−V(Y1,…,Yn) are given under various restrictions on c and n.

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Holger Kösters. "Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observations." Ann. Probab. 32 (4) 3324 - 3332, October 2004. https://doi.org/10.1214/009117904000000496

Information

Published: October 2004
First available in Project Euclid: 8 February 2005

zbMATH: 1078.60030
MathSciNet: MR2094447
Digital Object Identifier: 10.1214/009117904000000496

Subjects:
Primary: 60G40
Secondary: 60E15

Keywords: Optimal stopping , prophet inequality

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 4 • October 2004
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