Abstract
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 sum to 1 is the natural state space for the process. In fact, the complementary set acts like an entrance boundary.
Citation
Stewart Ethier. "A property of Petrov's diffusion." Electron. Commun. Probab. 19 1 - 4, 2014. https://doi.org/10.1214/ECP.v19-3684
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