A fragmentation process connected to Brownian motion

By Jean Bertoin. 2000

91 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/110307ce21bb0e7ed8ea44b5c62e7f2418f77d84

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In Management Science and Operations Research

In Mathematical Physics

Citations in the corpus

Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent (2000, background): “Bertoin [8] recently gave a different construction of the fragmentation process Y based on excursions of Brownian motion with varying drift.”
Self-similar fragmentations derived from the stable tree I (2003, background): “However, most of the fragmentation processes that have been extensively studied in recent years [3, 7 , 22, 9] do have known, and sometimes strange-looking semigroups involving conditioned Poisson clouds.”
The asymptotic behavior of fragmentation processes (2003, background): “We further refer to [5] for an alternative construction of the same fragmentation from the Brownian excursion, to [7] for another binary and non discrete self-similar fragmentation with negative index α = −1/2, which is also naturally connected to the Brownian excursion, and to [23,24] for other mor”
Poisson-Kingman partitions (2002, background): “…the two-parameter family to the lengths of excursions of a Markov process whose zero set is the range of a stable subordinator of index α. Section 8 provides further detail in the case α = j which corresponds to partitioning a time interval by the lengths of excursions of a Brownian motion.”
Combinatorial Stochastic Processes (2006, unknown): “See [42].”
Self-similar fragmentations derived from the stable tree II: splitting at nodes (2004, methodology): “According to [7] and [20], adding a drift to a certain class of Lévy processes allows to construct interesting fragmentations related to the entrance boundary of the stochastic additive coalescent.”