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arXiv · 2407.09102

Quantitative diffusion approximation for the Neutral $r$-Alleles Wright-Fisher Model with Mutations

Peng Chen·Jie Xiong·Lihu Xu·Jiayu Zheng
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Abstract

We apply a Lindeberg principle under the Markov process setting to approximate the Wright-Fisher model with neutral $r$-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 $r=2$ was studied.

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Peng Chen, Jie Xiong, Lihu Xu, Jiayu Zheng. 2024-07-12. Quantitative diffusion approximation for the Neutral $r$-Alleles Wright-Fisher Model with Mutations. https://arxiv.org/abs/2407.09102

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