TL;DR
This paper investigates a diffusion process in the Kingman simplex related to the two-parameter Poisson-Dirichlet distribution, revealing that certain boundary points act as entrance boundaries for the process.
Contribution
It demonstrates that the subset of the simplex with non-unit sum coordinates functions as an entrance boundary for Petrov's diffusion process.
Findings
The boundary subset acts as an entrance boundary.
The diffusion process is linked to the two-parameter Poisson-Dirichlet distribution.
Boundary behavior influences the process's long-term properties.
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 do not sum to 1 acts like an entrance boundary for the diffusion.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Stochastic processes and statistical mechanics · Diffusion and Search Dynamics