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Monte Carlo Algorithms for Finding the Maximum of a Random Walk with Negative Drift

Part of: Stochastic processes Theory of computing

Published online by Cambridge University Press:  14 July 2016

Ludwig Baringhaus  and
Rudolf Grübel
Ludwig Baringhaus*
Affiliation:
Universität Hannover
Rudolf Grübel*
Affiliation:
Universität Hannover
*
∗ Postal address: Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, Germany.
∗ Postal address: Institut für Mathematische Stochastik, Universität Hannover, Postfach 60 09, D-30060 Hannover, Germany.
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Abstract

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We discuss two Monte Carlo algorithms for finding the global maximum of a simple random walk with negative drift. This problem can be used to connect the analysis of random input Monte Carlo algorithms with ideas and principles from mathematical statistics.

Keywords

Brownian motion with driftconditioningefficiencyfast Fourier transformladder variableMarkov chainrandomization

MSC classification

Primary: 60G50: Sums of independent random variables; random walks 68Q25: Analysis of algorithms and problem complexity
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 74 - 86
Copyright
© Applied Probability Trust 2006 

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