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2020 Diffusions on a space of interval partitions: construction from Bertoin’s ${\tt BES}_{0}(d)$, $d\in (0,1)$
Matthias Winkel
Electron. Commun. Probab. 25: 1-13 (2020). DOI: 10.1214/20-ECP355

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 Lévy processes with index between 1 and 2 and with jumps marked by squared Bessel excursions of a corresponding dimension between $-2$ and 0.

Citation

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Matthias Winkel. "Diffusions on a space of interval partitions: construction from Bertoin’s ${\tt BES}_{0}(d)$, $d\in (0,1)$." Electron. Commun. Probab. 25 1 - 13, 2020. https://doi.org/10.1214/20-ECP355

Information

Received: 13 July 2020; Accepted: 9 October 2020; Published: 2020
First available in Project Euclid: 23 October 2020

Digital Object Identifier: 10.1214/20-ECP355

Subjects:
Primary: 60J25, 60J60, 60J80
Secondary: 60G18, 60G55

JOURNAL ARTICLE
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