2020/06/05 by Winkel, Matthias
#60G55 #60J60 #60J80 #FOS: Mathematics #Primary 60J25 #Probability (math.PR) #Secondary 60G18
paper · doi:10.48550/arxiv.2006.03587
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.