Fluctuation Theory of Continuous-Time, Skip-Free Downward Markov Chains with Applications to Branching Processes with Immigration

Ronnie Loeffen (), Pierre Patie () and Jian Wang ()
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Ronnie Loeffen: Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZL, United Kingdom
Pierre Patie: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853
Jian Wang: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853

Mathematics of Operations Research, 2025, vol. 50, issue 1, 169-188

Abstract: We develop a comprehensive methodology for the fluctuation theory of continuous-time, skip-free Markov chains, extending and improving the recent work of Choi and Patie for discrete-time, skip-free Markov chains. As a significant application, we use it to derive a full set of fluctuation identities regarding exiting a finite or infinite interval for Markov branching processes with immigration, thereby uncovering many new results for this classic family of continuous-time Markov chains. The theory also allows us to recover in a simple manner fluctuation identities for skip-free downward compound Poisson processes.

Keywords: Primary: 60J27; 60J45; 60J80; skip-free Markov chains; first passage time problems; fluctuation theory; branching processes with immigration; potential theory (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:1:p:169-188

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