The distribution of the spine of a Fleming-Viot type process

TL;DR

This paper proves the uniqueness of the spine in Fleming-Viot particle systems and characterizes its asymptotic behavior, including branching rates and distribution of side branches, under minimal assumptions.

Contribution

It establishes the uniqueness of the spine and describes its asymptotic branching behavior in Fleming-Viot processes with minimal assumptions.

Findings

Spine uniqueness under minimal assumptions

Asymptotic branching rate of twice that of generic particles

Distribution of side branches matches unconditioned branching tree

Abstract

We show uniqueness of the spine of a Fleming-Viot particle system under minimal assumptions on the driving process. If the driving process is a continuous time Markov process on a finite space, we show that asymptotically, when the number of particles goes to infinity, the branching rate for the spine is twice that of a generic particle in the system, and every side branch has the distribution of the unconditioned generic branching tree.