Exchangeable Markov Processes on (Formula presented.) with Cadlag Sample Paths

Harry Crane, Steven P. Lalley

Research output: Contribution to journalArticle

Abstract

Any exchangeable, time-homogeneous Markov processes on (Formula presented.) with cadlag sample paths projects to a Markov process on the simplex whose sample paths are cadlag and of locally bounded variation. Furthermore, any such process has a de Finetti-type description as a mixture of independent, identically distributed copies of time-inhomogeneous Markov processes on (Formula presented.). In the Feller case, these time-inhomogeneous Markov processes have a relatively simple structure; however, in the non-Feller case, a greater variety of behaviors is possible since the transition law of the underlying Markov process on (Formula presented.) can depend in a nontrivial way on its exchangeable (Formula presented.) -algebra.

Original languageEnglish (US)
Pages (from-to)206-230
Number of pages25
JournalJournal of Theoretical Probability
Volume29
Issue number1
DOIs
StatePublished - Mar 1 2016

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Keywords

  • Exchangeable random partition
  • Hewitt–Savage theorem
  • Interacting particle system
  • Paintbox process
  • de Finetti’s theorem

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