Quasi-stationary distributions for single death processes with killing
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916353044119552 |
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| author | Fang, Zhe-Kang Mao, Yong-Hua |
| author_facet | Fang, Zhe-Kang Mao, Yong-Hua |
| contents | 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 $\{1,2,3,\cdots\}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-stationary distributions for single death processes with killing Fang, Zhe-Kang Mao, Yong-Hua Probability 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 $\{1,2,3,\cdots\}$ 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. |
| title | Quasi-stationary distributions for single death processes with killing |
| topic | Probability |
| url | https://arxiv.org/abs/2408.05662 |