Year: 2023
Type: preprint
Abstract: In this work, we develop excursion theory for the Wright--Fisher diffusion with mutation. Our construction is intermediate between the classical excursion theory where all excursions begin and end at a single point and the more general approach considering excursions of processes from general sets. Since the Wright--Fisher diffusion has two boundary points, it is natural to construct excursions which start from a specified boundary point, and end at one of two boundary points which determine the next starting point. In order to do this we study the killed Wright--Fisher diffusion, which is sent to a cemetery state whenever it hits either endpoint. We then construct a marked Poisson process of such killed paths which, when concatenated, produce a pathwise construction of the Wright--Fisher diffusion.
Source: arXiv (Cornell University)
Authors: Jenkins, Paul A., Koskela, Jere, Rivero, Victor M., Sant, Jaromir, Spano, Dario, Valentic, Ivana
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1309768829, Geometric properties and potential theory of stochastic processes, G1633672591, G2932985130, G3855435662, G444630160, The Alan Turing Institute, Using hidden genealogical structure to study the architecture of human disease, Mathematical foundations of non-reversible MCMC for genome-scale inference
OpenAlex ID: W4387220742