Ergodic Inequality of Three Population Genetic Models

TL;DR

This paper derives new transition density representations and establishes ergodic inequalities for three population genetic models, enhancing understanding of their long-term behavior.

Contribution

It introduces novel representations of transition densities and provides ergodic inequalities for three key population genetic models, advancing theoretical understanding.

Findings

New transition density representations for two models

Ergodic inequalities established for all three models

Enhanced theoretical understanding of model long-term behavior

Abstract

In this article, three models are considered, they are the infinitely-many-neutral-alleles model \cite{MR615945}, infinite dimensional diffusion associated with two-parameter Poisson-Dirichlet distribution \cite{MR2596654} and the infinitely-many-alleles model with symmetric dominance \cite{MR1626158}. The new representations of the transition transition densities are obtained for the first two models. Lastly, the ergodic inequalities of these three models are provided.