## Poisson-Kingman Partitions (2002)

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Venue: | of Lecture Notes-Monograph Series |

Citations: | 11 - 3 self |

### BibTeX

@INPROCEEDINGS{Pitman02poisson-kingmanpartitions,

author = {Jim Pitman},

title = {Poisson-Kingman Partitions},

booktitle = {of Lecture Notes-Monograph Series},

year = {2002},

pages = {1--34}

}

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### 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 subordinator. 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.