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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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

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

First available in Project Euclid: 25 November 2003

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Zentralblatt MATH identifier

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

Analysis of algorithms searching random walk stochastic order Brownian motion


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.

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