Markov processes on the infinite-dimensional simplex
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
My talk is devoted to the family of markov processes on the infinite-dimensional simplex, initially constructed as the infinitely-many-neutral-allels diffusion model by Ethier and Kurth in 1981, and later generalised by Petrov, Borodin and Olshanski. These are Feller processes which are defined infinitesimally in terms of generators (operators acting on the space of functions on the simplex). I will describe several global properties which can be recovered form the infinitesimal definition and explain how these properties follow from the study of the generators.