Electronic Communications in Probability

A property of Petrov's diffusion

Stewart Ethier

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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.

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 65, 4 pp.

Dates
Accepted: 18 September 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316767

Digital Object Identifier
doi:10.1214/ECP.v19-3684

Mathematical Reviews number (MathSciNet)
MR3262071

Zentralblatt MATH identifier
1303.60068

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]

Keywords
infinite-dimensional diffusion process transition density two-parameter Poisson–Dirichlet distribution entrance boundary

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Ethier, Stewart. A property of Petrov's diffusion. Electron. Commun. Probab. 19 (2014), paper no. 65, 4 pp. doi:10.1214/ECP.v19-3684. https://projecteuclid.org/euclid.ecp/1465316767


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