Diffusions on a space of interval partitions: construction from Bertoin's ${\tt BES}_0(d)$, $d\in(0,1)$
Probability
2020-06-08 v1
Abstract
In 1990, Bertoin constructed a measure-valued Markov process in the framework of a Bessel process of dimension between 0 and 1. In the present paper, we represent this process in a space of interval partitions. We show that this is a member of a class of interval partition diffusions introduced recently and independently by Forman, Pal, Rizzolo and Winkel using a completely different construction from spectrally positive stable L\'evy processes with index between 1 and 2 and with jumps marked by squared Bessel excursions of a corresponding dimension between and 0.
Cite
@article{arxiv.2006.03587,
title = {Diffusions on a space of interval partitions: construction from Bertoin's ${\tt BES}_0(d)$, $d\in(0,1)$},
author = {Matthias Winkel},
journal= {arXiv preprint arXiv:2006.03587},
year = {2020}
}
Comments
12 pages, 1 figure