## Excursion theory of Wright-Fisher diffusions

I will illustrate aspects of excursion theory for the neutral Wright--Fisher diffusion with recurrent mutation. The structure 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. Several identities for excursion measures and hitting time distributions will be described both via special function theory and via the coalescent dual.

Area: CS13 - Diffusion and coalescent processes in population genetics (Martina Favero)

Keywords: Diffusion excursion theory, stochastic duality, Wright-Fisher diffusion, Kingman coalescent, Population genetics, Hypergeometric functions

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