The cut-and-paste process

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12 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 languageEnglish (US)
Pages (from-to)1952-1979
Number of pages28
JournalAnnals of Probability
Volume42
Issue number5
DOIs
StatePublished - 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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