# Fleming–Viot Particle System Driven by a Random Walk on $$\mathbb {N}$$N

@article{Maric2015FlemingViotPS,
title={Fleming–Viot Particle System Driven by a Random Walk on \$\$\mathbb \{N\}\$\$N},
author={Nevena Maric},
journal={Journal of Statistical Physics},
year={2015},
volume={160},
pages={548-560}
}
• N. Maric
• Published 1 May 2014
• Physics, Mathematics
• Journal of Statistical Physics
A random walk on $${\mathbb N}$$N with negative drift and absorption at 0, when conditioned on survival, has uncountably many invariant measures (quasi-stationary distributions, qsd ) $$\nu _c$$νc. We study a Fleming–Viot (fv ) particle system driven by this process. Simulation results indicate that mean normalized densities of the fv  unique stationary measure converge to the minimal qsd , $$\nu _0$$ν0, as $$N \rightarrow \infty$$N→∞. Furthermore, every other qsd of the random walk ($$\nu _c… 7 Citations ## Figures from this paper Minimal quasi-stationary distribution approximation for a birth and death process In a first part, we prove a Lyapunov-type criterion for the \xi_1-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal Fleming-Viot processes : two explicit examples • Mathematics • 2016 The purpose of this paper is to extend the investigation of the Fleming-Viot process in discrete space started in a previous work to two specific examples. The first one corresponds to a random walk Birth and Death process in mean field type interaction The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of A Non-Conservative Harris' Ergodic Theorem • Mathematics • 2019 We consider non-conservative positive semigroups and obtain necessary and sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Bootstrap maximum likelihood for quasi-stationary distributions • Mathematics Journal of Nonparametric Statistics • 2018 ABSTRACT Quasi-stationary distributions have many applications in diverse research fields. We develop a bootstrap-based maximum likelihood (BML) method to deal with quasi-stationary distributions in Processus de Fleming-Viot, distributions quasi-stationnaires et marches aléatoires en interaction de type champ moyen Dans cette these nous etudions le comportement asymptotique de systemes de particules en interaction de type champ moyen en espace discret, systemes pour lesquels l'interaction a lieu par Dynamics of a Fleming–Viot type particle system on the cycle graph This work is devoted to the study of interacting asymmetric continuous time random walks on the cycle graph, with uniform killing. The process is of Fleming-Viot or Moran type and allows to ## References SHOWING 1-10 OF 19 REFERENCES Quasi Stationary Distributions and Fleming-Viot Processes in Countable Spaces • Mathematics, Physics • 2007 We consider an irreducible pure jump Markov process with rates Q=(q(x,y)) on \Lambda\cup\{0\} with \Lambda countable and 0 an absorbing state. A {\em quasi stationary distribution \rm} (QSD) Metastability of reversible condensed zero range processes on a finite set • Mathematics • 2009 Let$${r: S\times S\to \mathbb R_{+}}$$be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m. For α > 1, let$${g: \mathbb N\to
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