Lumpability and Commutativity of Markov Processes

Authors: Jianjun Paul Tian ^a; D. Kannan ^b

Affiliations:	^a Mathematical Biosciences Institute, The Ohio State University, Columbus, Ohio, USA
	^b Department of Mathematics, University of Georgia, Athens, Georgia, USA

DOI: 10.1080/07362990600632045

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 24, Issue 3 July 2006 , pages 685 - 702

Subjects: Statistics & Probability; Stochastic Models & Processes;

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Abstract

We introduce the concepts of lumpability and commutativity of a continuous time discrete state space Markov process, and provide a necessary and sufficient condition for a lumpable Markov process to be commutative. Under suitable conditions we recover some of the basic quantities of the original Markov process from the jump chain of the lumped Markov process.

Keywords: Commutativity; Lumpability; Markov process

Mathematics Subject Classification: 60J10; 60J27; 60J75

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Lumpability and Commutativity of Markov Processes

Abstract