The Annals of Probability

The cut-and-paste process

Harry Crane

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Abstract

We characterize the class of exchangeable Feller processes evolving on partitions with boundedly many blocks. In continuous-time, the jump measure decomposes into two parts: a $\sigma$-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a Lévy–Itô representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices.

Article information

Source
Ann. Probab., Volume 42, Number 5 (2014), 1952-1979.

Dates
First available in Project Euclid: 29 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1409319471

Digital Object Identifier
doi:10.1214/14-AOP922

Mathematical Reviews number (MathSciNet)
MR3262496

Zentralblatt MATH identifier
1317.60034

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G09: Exchangeability 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Keywords
Exchangeable random partition de Finetti’s theorem Lévy–Itô decomposition paintbox process coalescent process interacting particle system Feller process random matrix product

Citation

Crane, Harry. The cut-and-paste process. Ann. Probab. 42 (2014), no. 5, 1952--1979. doi:10.1214/14-AOP922. https://projecteuclid.org/euclid.aop/1409319471


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References

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