Quasi-stationary distributions for continuous-time $\lambda$-recurrent jump processes

Qian Du; Yong-Hua Mao

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arXiv · 2407.19803

Quasi-stationary distributions for continuous-time $\lambda$-recurrent jump processes

Qian Du·Yong-Hua Mao

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Abstract

For the continuous-time $\lambda$-recurrent jump process, the $\lambda$-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.

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Qian Du, Yong-Hua Mao. 2024-07-29. Quasi-stationary distributions for continuous-time $\lambda$-recurrent jump processes. https://arxiv.org/abs/2407.19803

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