A difference prophet inequality for bounded i.i.d. variables, with cost for observations
type: Item
instance of: scholarly article
title: A difference prophet inequality for bounded i.i.d. variables, with cost for observations
zbMATH Open document ID: 0777.60035
author: Ester Samuel-Cahn
published in: The Annals of Probability
publication date: 1993-01-17T00:00:00Z
review text: The class of the difference prophet inequalities for the sequence of random variables \(Y_ i=X_ i-ic\), \(i=1,2,\dots\), where \(X_ i\), \(i=1,2,\dots\), are i.i.d. random variables such that \(0\leq X_ i\leq 1\) is studied. The comparison with the strictly related results of \textit{M. Jones} [J. Multivariate Anal. 34, No. 2, 238-253 (1990; Zbl 0753.60042)] for the case when \(X_ i\), \(i=1,2,\dots\), are independent random variables is given. The review of the prophet problems in the optimal stopping can be found in the paper by \textit{T. P. Hill} and \textit{R. P. Kertz} [Strategies for sequential search and selection in real time, Proc. Conf., Amherst/MA (USA) 1990, Contemp. Math. 125, 191-207 (1992)].
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 62L15
zbMATH DE Number: 97393
zbMATH Keywords: prophet inequality
zbMATH Keywords: cost of observation
zbMATH Keywords: stopping time
zbMATH Keywords: sharp inequalities for stochastic sequences
reviewed by: Krzysztof J. Szajowski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989689
OpenAlex ID: W2019745365
DOI: 10.1214/AOP/1176989689
description: scientific article; zbMATH DE number 97393