论文标题
复制器 - 突出器方程的概率分析
Probabilistic Analysis of Replicator-Mutator Equations
论文作者
论文摘要
本文在多维健身空间上介绍了一类复制器 - 突击器方程。我们通过使用Fockker-Planck-Kolmogorov（FPK）方程和Martingale提取方法来建立方程弱解的新型概率表示。提供了具有现有文献中考虑的不同适应性功能的封闭形式概率解决方案的示例。我们还构建了一个粒子系统，并证明了与与扩展复制器 - 突变器方程相关的FPK方程的任何解决方案，相对于适合我们概率的框架的类似于Wasserstein的距离。
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.
