On a New Characterization of Harris Recurrence for Markov Chains and Processes

Peter Glynn () and Yanlin Qu
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Peter Glynn: Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, USA
Yanlin Qu: Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, USA

Mathematics, 2023, vol. 11, issue 9, 1-7

Abstract: This paper shows that Harris recurrent Markov chains and processes can be characterized as the class of Markov chains and processes for which there exists a random time T at which the distribution of the chain or process does not depend on its initial condition. In particular, no independence assumptions concerning the post- T process or T play a role in the characterization. Since Harris chains and processes are known to contain infinite sequences of regeneration times exhibiting various independence properties, it follows that the existence of this single T implies the existence of infinitely many times at which regeneration occurs.

Keywords: regeneration; Harris recurrence; Markov chains; Markov processes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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