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- W3011300501 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." @default.
- W3011300501 created "2020-03-23" @default.
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- W3011300501 date "2020-03-11" @default.
- W3011300501 modified "2023-09-23" @default.
- W3011300501 title "Probabilistic Analysis of Replicator-Mutator Equations" @default.
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- W3011300501 doi "https://doi.org/10.48550/arxiv.2003.05143" @default.
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