Quasi-Stationary Distributions for Single Death Processes with Killing

Zhe-Kang Fang () and Yong-Hua Mao ()
Additional contact information
Zhe-Kang Fang: School of Mathematics and Statistics, Fujian Normal University
Yong-Hua Mao: School of Mathematics and Statistics, Fujian Normal University

Journal of Theoretical Probability, 2025, vol. 38, issue 3, 1-51

Abstract: Abstract This paper studies the quasi-stationary distributions for a single death process (or downwardly skip-free process) with killing defined on the nonnegative integers, corresponding to a non-conservative transition rate matrix. The set $$\{1,2,3,\ldots \}$$ { 1 , 2 , 3 , … } constitutes an irreducible class, and 0 is an absorbing state. For the single death process with three kinds of killing term, we obtain the existence and uniqueness of the quasi-stationary distribution. Moreover, we derive the conditions for exponential convergence to the quasi-stationary distribution in the total variation norm. Our main approach is based on the Doob’s h-transform, potential theory and probabilistic methods.

Keywords: Quasi-stationary distribution; Single death processes with killing; Potential theory; Doob’s h-transform; 60J27; 60F99 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-025-01429-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:38:y:2025:i:3:d:10.1007_s10959-025-01429-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-025-01429-6

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().