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Uniform in time propagation of chaos for a Moran model. Stoch Process Their Appl 2022. [DOI: 10.1016/j.spa.2022.09.006] [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: 11/23/2022]
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Berestycki J, Brunet É, Nolen J, Penington S. Brownian bees in the infinite swarm limit. ANN PROBAB 2022. [DOI: 10.1214/22-aop1578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Éric Brunet
- Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Cité
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Bhattacharya A, Palmowski Z, Zwart B. Persistence of heavy-tailed sample averages: principle of infinitely many big jumps. ELECTRON J PROBAB 2022. [DOI: 10.1214/22-ejp774] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Kolb M, Liesenfeld M. On non-extinction in a Fleming-Viot-type particle model with Bessel drift. ELECTRON J PROBAB 2022. [DOI: 10.1214/22-ejp866] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Yaglom limit for stochastic fluid models. ADV APPL PROBAB 2021. [DOI: 10.1017/apr.2020.71] [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
AbstractIn this paper we analyse the limiting conditional distribution (Yaglom limit) for stochastic fluid models (SFMs), a key class of models in the theory of matrix-analytic methods. So far, only transient and stationary analyses of SFMs have been considered in the literature. The limiting conditional distribution gives useful insights into what happens when the process has been evolving for a long time, given that its busy period has not ended yet. We derive expressions for the Yaglom limit in terms of the singularity˜$s^*$ such that the key matrix of the SFM, ${\boldsymbol{\Psi}}(s)$, is finite (exists) for all $s\geq s^*$ and infinite for $s<s^*$. We show the uniqueness of the Yaglom limit and illustrate the application of the theory with simple examples.
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Corujo J. Dynamics of a Fleming–Viot type particle system on the cycle graph. Stoch Process Their Appl 2021. [DOI: 10.1016/j.spa.2021.02.001] [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: 11/28/2022]
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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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Groisman P, Soprano-Loto N. Rank dependent branching-selection particle systems. ELECTRON J PROBAB 2021. [DOI: 10.1214/21-ejp724] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Pablo Groisman
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales and IMAS-CONICET, Argentina
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Villemonais D. Minimal quasi-stationary distribution approximation for a birth and death process. ELECTRON J PROBAB 2015. [DOI: 10.1214/ejp.v20-3482] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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