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On recurrent properties of Fisher--Wright's diffusion on (0,1) with mutation

Roman Sineokiy and Alexander Veretennikov

Abstract

A one-dimensional Fisher–Wright diffusion process on the interval ( 0 , 1 ) with mutations is considered. This is a widely known model in population genetics. The goal of this paper is an exponential recurrence of the process, which also implies an exponential rate of convergence towards the invariant measure.

MSC 2010: 60J60; 37A25

Communicated by Nikolai Leonenko


Funding source: Russian Science Foundation

Award Identifier / Grant number: 17-11-0198

Funding statement: For the second author of this study, part of Proposition 2.3 was prepared within the framework of the HSE University Basic Research Program, and part of Corollary 2.2 it was funded by the Russian Science Foundation grant 17-11-0198 (extended).

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Received: 2021-05-05
Accepted: 2021-05-10
Published Online: 2021-08-08
Published in Print: 2021-09-01

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