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Sharp asymptotic results for simplified mutation-selection algorithms. (English) Zbl 1036.60026

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

MSC:

60F17 Functional limit theorems; invariance principles
60F10 Large deviations
92D15 Problems related to evolution
60F05 Central limit and other weak theorems

Software:

MersenneTwister
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References:

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