The Spine of the Fleming-Viot process driven by Brownian motion

TL;DR

This paper proves that the spine of a Fleming-Viot process driven by Brownian motion in a bounded Lipschitz domain converges to a Brownian motion conditioned to stay within the domain indefinitely.

Contribution

It establishes a convergence result for the spine of the Fleming-Viot process in Lipschitz domains, linking it to conditioned Brownian motion.

Findings

Spine converges to conditioned Brownian motion.

Results apply to Lipschitz domains with Lipschitz constant less than 1.

Provides new insights into the behavior of Fleming-Viot processes.

Abstract

We show that the spine of the Fleming-Viot process driven by Brownian motion in a bounded Lipschitz domain with Lipschitz constant less than 1 converges to Brownian motion conditioned to stay in the domain forever.