Hitting times, number of jumps, and occupation times for continuous-time finite state Markov chains

David B. Colwell

Statistics & Probability Letters, 2023, vol. 195, issue C

Abstract: In this paper we discuss three random variables associated with a finite state continuous-time Markov chain having a constant transition rate matrix: the number of jumps between two different states, the amount of time spent in a given state, known as an occupation time, and the time it takes for the Markov chain to first reach a particular state, known as a hitting time or first passage time. First, we calculate expected values for each of these random variables. We then derive the moment generating functions for these variables. Our approach is to use the vector/matrix representations of the various processes. Each solution is written in terms of an integral of the exponential of a matrix.

Keywords: First hitting time; Occupation time; Hadamard product; Compensator; Synchronous jumps; Double regime-switching model (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109786

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