Abstract
For the birth—death Q-matrix with regular boundary, its minimal process and its maximal process are closely related. In this paper, we obtain the uniform decay rate and the quasi-stationary distribution for the minimal process. And via the construction theory, we mainly derive the eigentime identity and the distribution of the fastest strong stationary time (FSST) for the maximal process.
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The authors would like to thank the reviewers for their helpful comments.
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Supported by the National Natural Science Foundation of China (Grant Nos. 11501531, 11701265, 11771047)
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Gao, W.J., Mao, Y.H. & Zhang, C. The Birth–death Processes with Regular Boundary: Stationarity and Quasi-stationarity. Acta. Math. Sin.-English Ser. 38, 890–906 (2022). https://doi.org/10.1007/s10114-022-0567-y
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DOI: https://doi.org/10.1007/s10114-022-0567-y
Keywords
- Birth-death process
- regular boundary
- eigenvalue
- hitting time
- strong stationary time
- quasi-stationary distribution