Fluctuation theory of continuous-time skip-free downward Markov chains with applications to branching processes with immigration

R. Loeffen; P. Patie; J. Wang

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arXiv · 2208.14425

Fluctuation theory of continuous-time skip-free downward Markov chains with applications to branching processes with immigration

R. Loeffen·P. Patie·J. Wang

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Abstract

We develop a new methodology for the fluctuation theory of continuous-time skip-free Markov chains, extending the recent work of Choi and Patie [5] for discrete-time skip-free Markov chains. As the main 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 classical 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.

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BibTeX RIS

R. Loeffen, P. Patie, J. Wang. 2022-08-30. Fluctuation theory of continuous-time skip-free downward Markov chains with applications to branching processes with immigration. https://arxiv.org/abs/2208.14425

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