Fluctuation Theory of Continuous-Time, Skip-Free Downward Markov Chains with Applications to Branching Processes with Immigration
成果类型：
Article
署名作者：
Loeffen, Ronnie; Patie, Pierre; Wang, Jian
署名单位：
University of Liverpool; Cornell University
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2022.0246
发表日期：
2025
关键词：
摘要：
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.