# 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} }

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… Expand

#### Figures from this paper

#### 7 Citations

Minimal quasi-stationary distribution approximation for a birth and death process

- Mathematics
- 2014

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… Expand

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… Expand

Birth and Death process in mean field type interaction

- Mathematics
- 2015

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… Expand

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… Expand

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… Expand

Processus de Fleming-Viot, distributions quasi-stationnaires et marches aléatoires en interaction de type champ moyen

- Physics
- 2015

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… Expand

Dynamics of a Fleming–Viot type particle system on the cycle graph

- Mathematics
- 2020

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… Expand

#### 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)… Expand

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… Expand

Quasistationary Distributions and Fleming-Viot Processes in Finite Spaces

- Mathematics
- Journal of Applied Probability
- 2011

Consider a continuous-time Markov process with transition rates matrix Q in the state space Λ ⋃ {0}. In the associated Fleming-Viot process N particles evolve independently in Λ with transition rates… Expand

Minimal quasi-stationary distribution approximation for a birth and death process

- Mathematics
- 2014

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… Expand

Fleming-Viot selects the minimal quasi-stationary distribution: The Galton-Watson case

- Mathematics
- 2012

Consider N particles moving independently, each one according to a subcritical continuous-time Galton-Watson process unless it hits 0, at which time it jumps instantaneously to the position of one of… Expand

A note on the rightmost particle in a Fleming-Viot process

- Mathematics
- 2012

We consider N nearest neighbor random walks on the positive integers with a drift towards the origin. When one walk reaches the origin, it jumps to the position of one of the other N-1 walks, chosen… Expand

A Fleming–Viot Particle Representation¶of the Dirichlet Laplacian

- Mathematics
- 2000

Abstract: We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different… Expand

T. E. Harris’ contributions to interacting particle systems and percolation

- Mathematics
- 2011

This is a bird’s eye view of T. E. Harris’ work on interacting particle systems and percolation, and of its impact on later work in probability theory and mathematical physics. nal illness and death… Expand

EXISTENCE OF QUASI-STATIONARY DISTRIBUTIONS. A RENEWAL DYNAMICAL APPROACH

- Mathematics
- 1995

We consider Markov processes on the positive integers for which the origin is an absorbing state. Quasi-stationary distributions (qsd's) are described as fixed points of a transformation Φ in the… Expand

Simulation of quasi-stationary distributions on countable spaces

- Mathematics
- 2012

Quasi-stationary distributions (QSD) have been widely studied since the pioneering work of Kolmogorov (1938), Yaglom (1947) and Sevastyanov (1951). They appear as a natural object when considering… Expand