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November 2020 Long-time limits and occupation times for stable Fleming–Viot processes with decaying sampling rates
Michael A. Kouritzin, Khoa Lê
Ann. Inst. H. Poincaré Probab. Statist. 56(4): 2595-2620 (November 2020). DOI: 10.1214/20-AIHP1051

Abstract

A class of Fleming–Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are developed, addressing the question of long-time population distribution for growing populations. Asymptotics in higher orders are investigated. Convergence of particle location occupation and inhabitation time processes are also addressed and related by way of the historical process. The basic results and techniques allow general Feller motion/mutation and may apply to other measure-valued Markov processes.

Dans cet article, nous introduisons et analysons une classe de processus de Fleming–Viot, avec taux d’échantillonnage décroissant et déplacement $\alpha$-stable, correspondant à des distributions de populations croissantes. Les théorèmes limites en temps long presque-sûr pour ces processus sont obtenus, répondant ainsi à la question de la distribution en temps long de la population dans le cas de populations croissantes. Les asymptotiques d’ordres supérieurs sont aussi obtenues. Les convergences des processus de temps d’occupation et d’habitation des particules sont considérées et reliées au moyen du processus historique. Les résultats et techniques autorisent des processus de Feller de déplacement/mutation généraux et peuvent s’appliquer à d’autres processus de Markov à valeurs mesures.

Citation

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Michael A. Kouritzin. Khoa Lê. "Long-time limits and occupation times for stable Fleming–Viot processes with decaying sampling rates." Ann. Inst. H. Poincaré Probab. Statist. 56 (4) 2595 - 2620, November 2020. https://doi.org/10.1214/20-AIHP1051

Information

Received: 23 May 2017; Revised: 22 September 2019; Accepted: 20 February 2020; Published: November 2020
First available in Project Euclid: 21 October 2020

MathSciNet: MR4164849
Digital Object Identifier: 10.1214/20-AIHP1051

Subjects:
Primary: 60F15, 60J80
Secondary: 60B10, 60G57

Rights: Copyright © 2020 Institut Henri Poincaré

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Vol.56 • No. 4 • November 2020
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