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November 2003 A stochastically quasi-optimal search algorithm for the maximum of the simple random walk
P. Chassaing, J. F. Marckert, M. Yor
Ann. Appl. Probab. 13(4): 1264-1295 (November 2003). DOI: 10.1214/aoap/1069786499

Abstract

Odlyzko [Random Structures Algorithms 6 (1995) 275-295] exhibited an asymptotically optimal algorithm, with respect to the average cost, among algorithms that find the maximum of a random walk by using only probes and comparisons. We extend Odlyzko's techniques to prove that his algorithm is indeed asymptotically optimal in distribution (with respect to the stochastic order). We also characterize the limit law of its cost. Computing its moments in two ways allows us to recover a surprising identity concerning Euler sums.

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P. Chassaing. J. F. Marckert. M. Yor. "A stochastically quasi-optimal search algorithm for the maximum of the simple random walk." Ann. Appl. Probab. 13 (4) 1264 - 1295, November 2003. https://doi.org/10.1214/aoap/1069786499

Information

Published: November 2003
First available in Project Euclid: 25 November 2003

zbMATH: 1084.68145
MathSciNet: MR2023877
Digital Object Identifier: 10.1214/aoap/1069786499

Subjects:
Primary: 60J65 , 68Q25
Secondary: 60F17 , 68P10 , 90B40

Keywords: analysis of algorithms , Brownian motion , Random walk , searching , stochastic order

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 4 • November 2003
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