Quasi-stationary distributions for single death processes with killing

2024/08/11 by Zhe-Kang Fang, Fang, Zhe-Kang, Yong-Hua Mao +1
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2408.05662

openalex publication_date 2024/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies the quasi-stationary distributions for a single death process (or downwardly skip-free process) with killing defined on the non-negative integers, corresponding to a non-conservative transition rate matrix. The set \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.

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