%0 Journal Article %1 pitman2003pkp %A Pitman, J. %D 2003 %I Institute of Mathematical Statistics %J Lecture Notes-Monograph Series %K Poisson_Dirichlet_distribution exchangeability excursions partitions reference sampling_formula %P 1--34 %T Poisson-Kingman partitions %U http://arxiv.org/pdf/math/0210396 %X 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.

@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 = {https://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 }