Diffusions on a space of interval partitions: construction from Bertoin's ${\tt BES}_0(d)$, $d\in(0,1)$

Matthias Winkel

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arXiv · 2006.03587

Diffusions on a space of interval partitions: construction from Bertoin's ${\tt BES}_0(d)$, $d\in(0,1)$

Matthias Winkel

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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 $-2$ and 0.

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BibTeX RIS

Matthias Winkel. 2020-06-05. Diffusions on a space of interval partitions: construction from Bertoin's ${\tt BES}_0(d)$, $d\in(0,1)$. https://arxiv.org/abs/2006.03587

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