# 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} }

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…

## 12 Citations

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

- Mathematics
- 2019

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

- MathematicsAnnales 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

- 2020

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

- MathematicsTheory 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

- MathematicsStochastic 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; }

- MathematicsESAIM: 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

- Computer Science
- 2018

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 ScienceSIAM/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

- MathematicsLatin 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…

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