Open Access
August 2015 Lipschitz partition processes
Harry Crane
Bernoulli 21(3): 1386-1411 (August 2015). DOI: 10.3150/14-BEJ607


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.


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Harry Crane. "Lipschitz partition processes." Bernoulli 21 (3) 1386 - 1411, August 2015.


Received: 1 September 2012; Revised: 1 September 2013; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 1329.60250
MathSciNet: MR3352048
Digital Object Identifier: 10.3150/14-BEJ607

Keywords: Coalescent process , de Finetti’s theorem , Exchangeable random partition , iterated random functions , Markov process , paintbox process , Poisson random measure

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 3 • August 2015
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