On the occupation measure of evolution models with vanishing mutations

Michel Benaïm, Mario Bravo and Mathieu Faure
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Michel Benaïm: Université de Neuchâtel = University of Neuchatel
Mario Bravo: Facultad de Administración y Economía [Santiago de Chile]
Mathieu Faure: Aix Marseille Univ, CNRS, AMSE, Marseille, France

No 2604, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: We study the almost sure convergence of the occupation measure of evolution models where mutation rates decrease over time. We show that if the mutation parameter vanishes at a controlled rate, then the empirical occupation measure converges almost surely to a specific invariant distribution of a limiting Markov chain. Our results are obtained through the analysis of a larger class of time-inhomogeneous Markov chains with finite states pace, where the control on the mutation parameter is explained by the energy barrier of the limit process. Additionally, we derive an explicit L1 convergence rate, explained through the tree-optimality gap, that may be of independent interest.

Keywords: Evolution models; Inhomogeneous Markov chain; Occupation measure; Energy barrier (search for similar items in EconPapers)
Date: 2026-02-01
Note: Working paper AMSE 2026-04
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