Hitting Times and Interlacing Eigenvalues: A Stochastic Approach Using Intertwinings

James Allen Fill () and Vince Lyzinski ()
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James Allen Fill: The Johns Hopkins University
Vince Lyzinski: The Johns Hopkins University

Journal of Theoretical Probability, 2014, vol. 27, issue 3, 954-981

Abstract: Abstract We develop a systematic matrix-analytic approach, based on intertwinings of Markov semigroups, for proving theorems about hitting-time distributions for finite-state Markov chains—an approach that (sometimes) deepens understanding of the theorems by providing corresponding sample-path-by-sample-path stochastic constructions. We employ our approach to give new proofs and constructions for two theorems due to Mark Brown, theorems giving two quite different representations of hitting-time distributions for finite-state Markov chains started in stationarity. The proof, and corresponding construction, for one of the two theorems elucidates an intriguing connection between hitting-time distributions and the interlacing eigenvalues theorem for bordered symmetric matrices.

Keywords: Markov chains; Hitting times; Interlacing eigenvalues; Intertwinings; Primary 60J10; Secondary 60J27; 15A18 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0457-9

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