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November 2003 Sharp asymptotic results for simplified mutation-selection algorithms
A. Bienvenüe, J. Bérard
Ann. Appl. Probab. 13(4): 1534-1568 (November 2003). DOI: 10.1214/aoap/1069786510

Abstract

We study the asymptotic behavior of a mutation--selection genetic algorithm on the integers with finite population of size $p\ge 1$. The mutation is defined by the steps of a simple random walk and the fitness function is linear. We prove that the normalized population satisfies an invariance principle, that a large-deviations principle holds and that the relative positions converge in law. After $n$ steps, the population is asymptotically around $\sqrt{n}$ times the position at time $1$ of a Bessel process of dimension $2p-1$.

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A. Bienvenüe. J. Bérard. "Sharp asymptotic results for simplified mutation-selection algorithms." Ann. Appl. Probab. 13 (4) 1534 - 1568, November 2003. https://doi.org/10.1214/aoap/1069786510

Information

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

zbMATH: 1036.60026
MathSciNet: MR2023888
Digital Object Identifier: 10.1214/aoap/1069786510

Subjects:
Primary: 60F05 , 60F10 , 60F17 , 92D15

Keywords: Genetic algorithm , interacting particle systems , invariance principle , large-deviations , Population dynamics , Random walks

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 4 • November 2003
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