Quasi-stationary distributions for continuous-time $λ$-recurrent jump processes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911971036626944 |
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| author | Du, Qian Mao, Yong-Hua |
| author_facet | Du, Qian Mao, Yong-Hua |
| contents | For the continuous-time $λ$-recurrent jump process, the $λ$-recurrence assures the existence of quasi-stationary distribution when it has finite exit states (the states that have positive killing rates). And we give an explicit representation for this quasi-stationary distribution through $Q$-matrix, where the components of the quasi-stationary distribution outside the set $H$ of exit states can be represented by those within $H$. Sufficient condition is also provided for quasi-stationary distribution when the exit states are infinite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19803 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-stationary distributions for continuous-time $λ$-recurrent jump processes Du, Qian Mao, Yong-Hua Probability For the continuous-time $λ$-recurrent jump process, the $λ$-recurrence assures the existence of quasi-stationary distribution when it has finite exit states (the states that have positive killing rates). And we give an explicit representation for this quasi-stationary distribution through $Q$-matrix, where the components of the quasi-stationary distribution outside the set $H$ of exit states can be represented by those within $H$. Sufficient condition is also provided for quasi-stationary distribution when the exit states are infinite. |
| title | Quasi-stationary distributions for continuous-time $λ$-recurrent jump processes |
| topic | Probability |
| url | https://arxiv.org/abs/2407.19803 |