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

TL;DR

This paper establishes a Central Limit Theorem for Fleming-Viot particle systems with hard killing, providing a rigorous statistical foundation for their approximation of Markov processes with killing under broad conditions.

Contribution

It proves a general CLT for Fleming-Viot systems with minimal assumptions, including elliptic diffusions with hard killing, extending previous results on their asymptotic behavior.

Findings

Proves CLT under broad conditions including non-explosion and atomless distributions.

Applicable to elliptic diffusions with hard killing.

Provides theoretical justification for large-sample approximations.

Abstract

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 context, each particle evolves independently according to the law of the underlying Markov process until its killing, and then branches instantaneously on another randomly chosen particle. While the consistency of this algorithm in the large population limit has been recently studied in several articles, our purpose here is to prove Central Limit Theorems under very general assumptions. For this, we only suppose that the particle system does not explode in finite time, and that the jump and killing times have atomless distributions. In particular, this includes the case of elliptic diffusions with hard killing.