Petrov constructed a diffusion process in the Kingman simplex whose unique stationary distribution is the two-parameter Poisson-Dirichlet distribution of Pitman and Yor. We show that the subset of the simplex comprising vectors whose coordinates do not sum to 1 acts like an entrance boundary for the diffusion.
Cite
@article{arxiv.1406.5198,
title = {A property of Petrov's diffusion},
author = {S. N. Ethier},
journal= {arXiv preprint arXiv:1406.5198},
year = {2015}
}