• Corpus ID: 119132951

# A Central Limit Theorem for Fleming-Viot Particle Systems with Soft Killing

@inproceedings{Crou2016ACL,
title={A Central Limit Theorem for Fleming-Viot Particle Systems with Soft Killing},
author={Fr{\'e}d{\'e}ric C{\'e}rou and Bernard Delyon and Arnaud Guyader and Mathias Rousset},
year={2016}
}
• Published 2 November 2016
• Mathematics
The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of the underlying Markov process, and branches onto another particle at each killing time. The consistency of this method in the large population limit was the subject of several recent articles. In the present paper, we go one step forward and prove a central…

### A Central Limit Theorem for Fleming-Viot Particle Systems 1

Fleming-Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this

### A central limit theorem for Fleming–Viot particle systems

• Mathematics
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 2020
The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is

### A central limit theorem for Fleming–Viot particle systems1

Fleming–Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this

### On synchronized Fleming–Viot particle systems

• Mathematics
Theory of Probability and Mathematical Statistics
• 2019
This article presents a variant of Fleming-Viot particle systems, which are a standard way to approximate the law of a Markov process with killing as well as related quantities. Classical

### Limit theorems for cloning algorithms

• Mathematics
Stochastic Processes and their Applications
• 2021

### Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: uniform estimates in a compact soft case. p, li { white-space: pre-wrap; }

• Mathematics
ESAIM: Probability and Statistics
• 2021
We establish the convergences (with respect to the simulation time $t$; the number of particles $N$; the timestep $\gamma$) of a Moran/Fleming-Viot type particle scheme toward the quasi-stationary

### PR ] 2 3 A pr 2 01 8 On the Asymptotic Normality of Adaptive Multilevel Splitting 1

The purpose of this paper is to prove both consistency and asymptotic normality results in a general setting by associating to the original Markov process a level-indexed process, and by showing that AMS can then be seen as a Fleming-Viot type particle system.

### Uniform convergence of the Fleming-Viot process in a hard killing metastable case

• Mathematics
• 2022
We study the long-time convergence of a Fleming-Viot process, in the case where the underlying process is a metastable diﬀusion killed when it reaches some level set. Through a coupling argument, we

### On the Asymptotic Normality of Adaptive Multilevel Splitting

• Computer Science
SIAM/ASA J. Uncertain. Quantification
• 2019
The purpose of this paper is to prove both consistency and asymptotic normality results in a general setting by associating to the original Markov process a level-indexed process, and by showing that AMS can then be seen as a Fleming-Viot type particle system.

### Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution

• Mathematics
Latin American Journal of Probability and Mathematical Statistics
• 2021
We prove under mild conditions that the Fleming-Viot process selects the minimal quasi-stationary distribution for Markov processes with soft killing on non-compact state spaces. Our results are

## References

SHOWING 1-10 OF 25 REFERENCES

### General approximation method for the distribution of Markov processes conditioned not to be killed

We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a

### Configurational transition in a Fleming - Viot-type model and probabilistic interpretation of Laplacian eigenfunctions

• Mathematics
• 1996
We analyse and simulate a two-dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in a

### Non-extinction of a Fleming-Viot particle model

• Mathematics
• 2009
We consider a branching particle model in which particles move inside a Euclidean domain according to the following rules. The particles move as independent Brownian motions until one of them hits

### Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering

• Mathematics
• 2000
This paper focuses on interacting particle systems methods for solving numerically a class of Feynman-Kac formulae arising in the study of certain parabolic differential equations, physics, biology,

### A stationary Fleming–Viot type Brownian particle system

We consider a system $${\{X_1,\ldots,X_N\}}$$ of N particles in a bounded d-dimensional domain D. During periods in which none of the particles $${X_1,\ldots,X_N}$$ hit the boundary $${\partial D}$$

### Piecewise-deterministic Markov Processes: A General Class of Non-diffusion Stochastic Models

Stochastic calculus for these stochastic processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper.

### A multiple replica approach to simulate reactive trajectories.

• Physics
The Journal of chemical physics
• 2011
A method to generate reactive trajectories, namely equilibrium trajectories leaving a metastable state and ending in another one is proposed. The algorithm is based on simulating in parallel many

### Continuous martingales and Brownian motion

• Mathematics
• 1990
0. Preliminaries.- I. Introduction.- II. Martingales.- III. Markov Processes.- IV. Stochastic Integration.- V. Representation of Martingales.- VI. Local Times.- VII. Generators and Time Reversal.-

### Limit Theorems for Stochastic Processes

• Mathematics
• 1987
I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems