Quasi-stationary distributions for subcritical branching Markov chains
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908541438132224 |
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| author | Hong, Wenming Yao, Dan |
| author_facet | Hong, Wenming Yao, Dan |
| contents | Consider a subcritical branching Markov chain. Let $Z_n$ denote the counting measure of particles of generation $n$. Under some conditions, we give a probabilistic proof for the existence of the Yaglom limit of $(Z_n)_{n\in\mathbb{N}}$ by the moment method, based on the spinal decomposition and the many-to-few formula. As a result, we give explicit integral representations of all quasi-stationary distributions of $(Z_n)_{n\in\mathbb{N}}$, whose proofs are direct and probabilistic, and don't rely on Martin boundary theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-stationary distributions for subcritical branching Markov chains Hong, Wenming Yao, Dan Probability Consider a subcritical branching Markov chain. Let $Z_n$ denote the counting measure of particles of generation $n$. Under some conditions, we give a probabilistic proof for the existence of the Yaglom limit of $(Z_n)_{n\in\mathbb{N}}$ by the moment method, based on the spinal decomposition and the many-to-few formula. As a result, we give explicit integral representations of all quasi-stationary distributions of $(Z_n)_{n\in\mathbb{N}}$, whose proofs are direct and probabilistic, and don't rely on Martin boundary theory. |
| title | Quasi-stationary distributions for subcritical branching Markov chains |
| topic | Probability |
| url | https://arxiv.org/abs/2405.04284 |