The cut-and-paste process

Harry Crane

doi:10.1214/14-AOP922

The cut-and-paste process

Harry Crane

SAS - Statistics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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 σ-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.

Original language	English (US)
Pages (from-to)	1952-1979
Number of pages	28
Journal	Annals of Probability
Volume	42
Issue number	5
DOIs	https://doi.org/10.1214/14-AOP922
State	Published - Sep 2014

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Coalescent process
De Finettis theorem
Exchangeable random partition
Feller process
Interacting particle system
Lévy-Ito̧ decomposition
Paintbox process
Random matrix product

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10.1214/14-AOP922

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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 σ-finite measure on stochastic matrices and a collection of nonnegative real constants. This decomposition prompts a L{\'e}vy-It{\^o} representation. In discrete-time, the evolution is described more simply by a product of independent, identically distributed random matrices.",

keywords = "Coalescent process, De Finettis theorem, Exchangeable random partition, Feller process, Interacting particle system, L{\'e}vy-It{\c o} decomposition, Paintbox process, Random matrix product",

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AB - 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 σ-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.

KW - Coalescent process

KW - De Finettis theorem

KW - Exchangeable random partition

KW - Feller process

KW - Interacting particle system

KW - Lévy-Ito̧ decomposition

KW - Paintbox process

KW - Random matrix product

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DO - 10.1214/14-AOP922

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SP - 1952

EP - 1979

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 5

ER -

The cut-and-paste process

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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