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Some diffusion processes associated with two parameter Poisson–Dirichlet distribution and Dirichlet process
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  • Published: 11 July 2009

Some diffusion processes associated with two parameter Poisson–Dirichlet distribution and Dirichlet process

  • Shui Feng1 &
  • Wei Sun2 

Probability Theory and Related Fields volume 148, pages 501–525 (2010)Cite this article

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Abstract

The two parameter Poisson–Dirichlet distribution PD(α, θ) is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman’s Poisson–Dirichlet distribution. The two parameter Dirichlet process \({\Pi_{\alpha,\theta,\nu_0}}\) is the law of a pure atomic random measure with masses following the two parameter Poisson–Dirichlet distribution. In this article we focus on the construction and the properties of the infinite dimensional symmetric diffusion processes with respective symmetric measures PD(α, θ) and \({\Pi_{\alpha,\theta,\nu_0}}\). The methods used come from the theory of Dirichlet forms.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, L8S 4K1, Canada

    Shui Feng

  2. Department of Mathematics and Statistics, Concordia University, Montreal, H3G 1M8, Canada

    Wei Sun

Authors
  1. Shui Feng
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  2. Wei Sun
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Correspondence to Shui Feng.

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Feng, S., Sun, W. Some diffusion processes associated with two parameter Poisson–Dirichlet distribution and Dirichlet process. Probab. Theory Relat. Fields 148, 501–525 (2010). https://doi.org/10.1007/s00440-009-0238-2

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  • Received: 21 March 2009

  • Revised: 10 June 2009

  • Published: 11 July 2009

  • Issue Date: November 2010

  • DOI: https://doi.org/10.1007/s00440-009-0238-2

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Mathematics Subject Classification (2000)

  • Primary: 60F10
  • Secondary: 92D10
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