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Champagnat N, Villemonais D. General criteria for the study of quasi-stationarity. ELECTRON J PROBAB 2023. [DOI: 10.1214/22-ejp880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
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Zhang H, Mo Y. Domain of attraction of quasi-stationary distribution for absorbing Markov processes. Stat Probab Lett 2022. [DOI: 10.1016/j.spl.2022.109692] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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Exponential convergence to a quasi-stationary distribution for birth–death processes with an entrance boundary at infinity. J Appl Probab 2022. [DOI: 10.1017/jpr.2021.100] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Abstract
We study the quasi-stationary behavior of the birth–death process with an entrance boundary at infinity. We give by the h-transform an alternative and simpler proof for the exponential convergence of conditioned distributions to a unique quasi-stationary distribution in the total variation norm. In addition, we also show that starting from any initial distribution the conditional probability converges to the unique quasi-stationary distribution exponentially fast in the
$\psi$
-norm.
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Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution. LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS 2021. [DOI: 10.30757/alea.v18-01] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Mailler C, Villemonais D. Stochastic approximation on noncompact measure spaces and application to measure-valued Pólya processes. ANN APPL PROBAB 2020. [DOI: 10.1214/20-aap1561] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Guo G, Allison J, Zhu L. Bootstrap maximum likelihood for quasi-stationary distributions. J Nonparametr Stat 2018. [DOI: 10.1080/10485252.2018.1531130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Guangbao Guo
- School of Mathematics and Statistics, Shandong University of Technology, Zibo, People's Republic of China
| | - James Allison
- Unit for Business Mathematics and Information, North-West University, Potchefstroom, South Africa
| | - Lixing Zhu
- Unit for Business Mathematics and Information, North-West University, Potchefstroom, South Africa
- Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
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