Lipschitz partition processes
Abstract
We introduce a family of Markov processes on set partitions with a bounded number of blocks, called Lipschitz partition processes. We construct these processes explicitly by a Poisson point process on the space of Lipschitz continuous maps on partitions. By this construction, the Markovian consistency property is readily satisfied; that is, the finite restrictions of any Lipschitz partition process comprise a compatible collection of finite state space Markov chains. We further characterize the class of exchangeable Lipschitz partition processes by a novel set-valued matrix operation.
Cite
@article{arxiv.1506.01495,
title = {Lipschitz partition processes},
author = {Harry Crane},
journal= {arXiv preprint arXiv:1506.01495},
year = {2015}
}
Comments
Published at http://dx.doi.org/10.3150/14-BEJ607 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)