A property of Petrov's diffusion

Stewart N. Ethier (University of Utah)

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.

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Pages: 1-4

Publication Date: September 18, 2014

DOI: 10.1214/ECP.v19-3684

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