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

Loeffen, Ronnie ORCID: 0000-0002-8461-6288, Patie, Pierre and Wang, J (2024) Fluctuation theory of continuous-time skip-free downward Markov chains with applications to branching processes with immigration. Mathematics of Operations Research.

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Official URL: http://dx.doi.org/10.1287/moor.2022.0246

Abstract

<jats:p> 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. </jats:p>

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	18 Jan 2024 08:51
Last Modified:	14 Mar 2024 08:41
DOI:	10.1287/moor.2022.0246
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3177890