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Poisson-Kingman partitions

by: J. Pitman

In: Lecture Notes-Monograph SeriesInstitute of Mathematical Statistics (2003) , p. 1--34.

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URL:	http://arxiv.org/pdf/math/0210396

This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the two-parameter family of Poisson-Dirichlet models derived from the Poisson process of jumps of a stable sub- ordinator. Applications are made to the random partition generated by the lengths of excursions of a Brownian motion or Brownian bridge conditioned on its local time at zero.

Description

{Poisson-Kingman partitions}

BibTeX record

@article{pitman2003pkp,
  abstract = {    This paper presents some general formulas for random partitions of a finite set
derived by Kingman's model of random sampling from an interval partition generated
by subintervals whose lengths are the points of a Poisson point process. These lengths
can be also interpreted as the jumps of a subordinator, that is an increasing process
with stationary independent increments. Examples include the two-parameter family
of Poisson-Dirichlet models derived from the Poisson process of jumps of a stable sub-
ordinator. Applications are made to the random partition generated by the lengths
of excursions of a Brownian motion or Brownian bridge conditioned on its local time
at zero.
},
  added-at = {2009-04-25T01:55:19.000+0200},
  author = {Pitman, J.},
  biburl = {http://www.bibsonomy.org/bibtex/2868b2332af933348e30042a963ace490/peter.ralph},
  description = {{Poisson-Kingman partitions}},
  interhash = {a630b147e8314ea6d732b75770f2fd90},
  intrahash = {868b2332af933348e30042a963ace490},
  journal = {Lecture Notes-Monograph Series},
  keywords = {Poisson_Dirichlet_distribution exchangeability excursions partitions reference sampling_formula},
  pages = {1--34},
  publisher = {Institute of Mathematical Statistics},
  timestamp = {2009-04-25T01:55:19.000+0200},
  title = {{Poisson-Kingman partitions}},
  url = {http://arxiv.org/pdf/math/0210396},
  year = 2003
}

Endnote record