Diffusions on a space of interval partitions: construction from Bertoin's ${\tt BES}_0(d)$, $d\in(0,1)$
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.03587
- arXiv:
- arXiv:2006.03587
- Bibcode:
- 2020arXiv200603587W
- Keywords:
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- Mathematics - Probability;
- Primary 60J25;
- 60J60;
- 60J80;
- Secondary 60G18;
- 60G55
- E-Print:
- 12 pages, 1 figure