A Unified Approach for Hitting Time of Jump Markov Type Processes

Nikolaos Limnios () and Bei Wu ()
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Nikolaos Limnios: Université de Technologie de Compiègne, Sorbonne University Alliance
Bei Wu: Northwestern Polytechnical University

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 3, 1-10

Abstract: Abstract This paper investigates the asymptotic analysis of the hitting time of Markov-type jump processes (i.e., semi-Markov, Markov, in continuous or discrete time) with a small probability of entering a non-empty terminal subset. This means that absorption is a rare event. The mean hitting time function of all four type processes obeyed the same equation. We obtain unified results of asymptotic approximation in a series scheme or, equivalently, a functional type of mean hitting time.

Keywords: Hitting time; Markov process; Markov chain; Phase-type distribution; Semi-Markov process; Semi-Markov chain; Rare event; 60J05; 60J25; 60K15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11009-024-10100-2

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