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.
%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
}