Exchangeable Markov Processes on $$[k]^{\mathbb N}$$ [ k ] N with Cadlag Sample Paths

Harry Crane and Steven P. Lalley ()
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Harry Crane: Rutgers University
Steven P. Lalley: University of Chicago

Journal of Theoretical Probability, 2016, vol. 29, issue 1, 206-230

Abstract: Abstract Any exchangeable, time-homogeneous Markov processes on $$[k]^{\mathbb {N}}$$ [ k ] N 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 $$[k]$$ [ k ] . 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 $$[k]^{\mathbb N}$$ [ k ] N can depend in a nontrivial way on its exchangeable $$\sigma $$ σ -algebra.

Keywords: Exchangeable random partition; de Finetti’s theorem; Hewitt–Savage theorem; Paintbox process; Interacting particle system; Primary 60J25; 60G09 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-014-0566-8

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