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Ranked fragmentations. (English) Zbl 1001.60078
Summary: We define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of these two types of fragmentations. We then give an explicit construction of homogeneous ranked fragmentations in terms of Poisson point processes. Finally we use this construction and classical results on records of Poisson point processes to study the small-time behavior of a ranked fragmentation.

MSC:
60J25 Continuous-time Markov processes on general state spaces
60G09 Exchangeability for stochastic processes
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