%0 Generic %1 arXiv:math.PR/0408071 %A Gnedin, Alexander %A Pitman, Jim %D 2004 %K author_pitman_from_arxiv %T Regenerative partition structures. %U http://arxiv.org/abs/math.PR/0408071 %X We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration after deletion of a part chosen by size-biased sampling. We associate each regenerative partition structure with a corresponding regenerative composition structure, which (as we showed in a previous paper) can be associated in turn with a regenerative random subset of the positive halfline, that is the closed range of a subordinator. A general regenerative partition structure is thus represented in terms of the Laplace exponent of an associated subordinator. We also analyse deletion properties characteristic of the two-parameter family of partition structures.

@misc{arXiv:math.PR/0408071, abstract = {We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration after deletion of a part chosen by size-biased sampling. We associate each regenerative partition structure with a corresponding regenerative composition structure, which (as we showed in a previous paper) can be associated in turn with a regenerative random subset of the positive halfline, that is the closed range of a subordinator. A general regenerative partition structure is thus represented in terms of the Laplace exponent of an associated subordinator. We also analyse deletion properties characteristic of the two-parameter family of partition structures.}, added-at = {2008-01-25T05:29:59.000+0100}, arxiv = {arXiv:math.PR/0408071}, author = {Gnedin, Alexander and Pitman, Jim}, biburl = {https://www.bibsonomy.org/bibtex/21cb63291d4ec2306763df8a252ac07ab/pitman}, interhash = {79228d0fdb6ac853013f6e0853c407d0}, intrahash = {1cb63291d4ec2306763df8a252ac07ab}, keywords = {author_pitman_from_arxiv}, timestamp = {2008-01-25T05:33:08.000+0100}, title = {{Regenerative partition structures.}}, url = {http://arxiv.org/abs/math.PR/0408071}, year = 2004 }