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arXiv · 2003.05143

Probabilistic Analysis of Replicator-Mutator Equations

Lijun Bo·Huafu Liao
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Abstract

This paper introduces a general class of Replicator-Mutator equations on a multi-dimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fockker-Planck-Kolmogorov (FPK) equations and a martingale extraction approach. The examples with closed-form probabilistic solutions for different fitness functions considered in the existing literature are provided. We also construct a particle system and prove a general convergence result to any solution to the FPK equation associated with the extended Replicator-Mutator equation with respect to a Wasserstein-like distance adapted to our probabilistic framework.

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Lijun Bo, Huafu Liao. 2020-03-13. Probabilistic Analysis of Replicator-Mutator Equations. https://arxiv.org/abs/2003.05143

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