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

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  • Colwell, David B.

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.

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  • Colwell, David B., 2023. "Hitting times, number of jumps, and occupation times for continuous-time finite state Markov chains," Statistics & Probability Letters, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s016771522300010x
    DOI: 10.1016/j.spl.2023.109786
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    References listed on IDEAS

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    1. Yang Shen & Kun Fan & Tak Kuen Siu, 2014. "Option Valuation Under a Double Regime‐Switching Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(5), pages 451-478, May.
    2. Donatien Hainaut & David B. Colwell, 2016. "A structural model for credit risk with switching processes and synchronous jumps," The European Journal of Finance, Taylor & Francis Journals, vol. 22(11), pages 1040-1062, September.
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