The Annals of Applied Probability

A stochastically quasi-optimal search algorithm for the maximum of the simple random walk

P. Chassaing, J. F. Marckert, and M. Yor

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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.

Article information

Source
Ann. Appl. Probab., Volume 13, Number 4 (2003), 1264-1295.

Dates
First available in Project Euclid: 25 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1069786499

Digital Object Identifier
doi:10.1214/aoap/1069786499

Mathematical Reviews number (MathSciNet)
MR2023877

Zentralblatt MATH identifier
1084.68145

Subjects
Primary: 68Q25: Analysis of algorithms and problem complexity [See also 68W40] 60J65: Brownian motion [See also 58J65]
Secondary: 60F17: Functional limit theorems; invariance principles 68P10: Searching and sorting 90B40: Search theory

Keywords
Analysis of algorithms searching random walk stochastic order Brownian motion

Citation

Chassaing, P.; Marckert, J. F.; Yor, M. A stochastically quasi-optimal search algorithm for the maximum of the simple random walk. Ann. Appl. Probab. 13 (2003), no. 4, 1264--1295. doi:10.1214/aoap/1069786499. https://projecteuclid.org/euclid.aoap/1069786499


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