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A Random Walk Version of Robbins' Problem

Robbins' problem is an optimal stopping problem where one seeks to minimize the expected rank of their observations among all observations. We examine random walk analogs to Robbins' problem in both discrete and continuous time. In discrete time, we consider full information and relative ranks versions of this problem. For three step walks, we give the optimal stopping rule and the expected rank for both versions. We also give asymptotic upper bounds for the expected rank in discrete time. Finally, we give upper and lower bounds for the expected rank in continuous time, and we show that the expected rank in the continuous time problem is at least as large as the normalized asymptotic expected rank in the full information discrete time version.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc1404568
Date12 1900
CreatorsAllen, Andrew
ContributorsAllaart, Pieter C., Quintanilla, John, Song, Kai-Sheng
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formativ, 55 pages, Text
RightsPublic, Allen, Andrew, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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