Regenerative partition structures
摘要
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.
关键词
引用
@article{arxiv.math/0408071,
title = {Regenerative partition structures},
author = {Alexander Gnedin and Jim Pitman},
journal= {arXiv preprint arXiv:math/0408071},
year = {2007}
}