Transition functions of diffusion processes with the Jack parameter on the Thoma simplex
Probability
2020-09-22 v3 Combinatorics
Abstract
The paper deals with a three-dimensional family of diffusion processes on an infinite-dimensional simplex. These processes were constructed by Borodin and Olshanski (arXiv:0706.1034; arXiv:0902.3395), and they include, as limit objects, the Ethier-Kurtz's infinitely-many-neutral-allels diffusion model (1981) and its extension found by Petrov (arXiv:0708.1930). Each process X from our family possesses a symmetrising measure M. Our main result is that the transition function of X has continuous density with respect to M. This is a generalization of earlier results due to Ethier (1992) and to Feng, Sun, Wang, and Xu (2011). Our proof substantially uses a special basis in the algebra of symmetric functions related to Laguerre polynomials.
Cite
@article{arxiv.1806.07454,
title = {Transition functions of diffusion processes with the Jack parameter on the Thoma simplex},
author = {Sergei Korotkikh},
journal= {arXiv preprint arXiv:1806.07454},
year = {2020}
}