Prophet inequalities for averages of independent non-negative random variables
type: Item
instance of: scholarly article
title: Prophet inequalities for averages of independent non-negative random variables
zbMATH Open document ID: 0604.60042
DOI: 10.1007/BF01164017
author: Theodore P. Hill
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173746
review text: Let \(X_ 1,X_ 2,..\). be independent nonnegative random variables, \(A_ n=(X_ 1+...+X_ n)/n\) and \(\Sigma_ n\) the set of stopping times \(\tau\) for \(X_ 1,X_ 2,...\). The author proves \[ E(\sup_{j\leq n}A_ j)\leq (2-1/n)\sup \{E(A_{\tau}): \tau \in \Sigma_ n\}. \] The constant (2-1/n) is sharp. (The reviewer and \textit{L. Sucheston} [Bull. Am. Math. Soc. 83, 745-747 (1977; Zbl 0336.60032)] had obtained the inequality with the weaker constant \(2(1+\sqrt{3})\), and the problem of obtaining the best possible constant had challenged quite a few mathematicians).
reviewed by: Ulrich Krengel
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 3976008
zbMATH Keywords: prophet inequality
zbMATH Keywords: stopping times
MaRDI profile type: Publication
cites work: Q5641856
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OpenAlex ID: W2091247129
description: scientific article; zbMATH DE number 3976008