Quantitative diffusion approximation for the Neutral $r$-Alleles Wright-Fisher Model with Mutations
Probability
2024-07-15 v1
Abstract
We apply a Lindeberg principle under the Markov process setting to approximate the Wright-Fisher model with neutral -alleles using a diffusion process, deriving an error rate based on a function class distance involving fourth-order bounded differentiable functions. This error rate consists of a linear combination of the maximum mutation rate and the reciprocal of the population size. Our result improves the error bound in the seminal work [PNAS,1977], where only the special case was studied.
Keywords
Cite
@article{arxiv.2407.09102,
title = {Quantitative diffusion approximation for the Neutral $r$-Alleles Wright-Fisher Model with Mutations},
author = {Peng Chen and Jie Xiong and Lihu Xu and Jiayu Zheng},
journal= {arXiv preprint arXiv:2407.09102},
year = {2024}
}