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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ronnie Loeffen & Pierre Patie & Jian Wang, 2025. "Fluctuation Theory of Continuous-Time, Skip-Free Downward Markov Chains with Applications to Branching Processes with Immigration," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 169-188, February.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:1:p:169-188
    DOI: 10.1287/moor.2022.0246
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