文章基本信息

标题：Diffusions on a space of interval partitions: construction from Bertoin’s ${\tt BES}_{0}(d)$, $d\in (0,1)$
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作者：Matthias Winkel
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2020
卷号：25
DOI：10.1214/20-ECP355
语种：English
出版社：Electronic Communications in Probability
摘要：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.
关键词：interval partition;Bessel process;measure-valued diffusion;Poisson–Dirichlet distribution;excursion theory