Titlebook: Combinatorial Stochastic Processes; Ecole d‘Eté de Proba Jim Pitman,Jean Picard Book 2006 Springer-Verlag Berlin Heidelberg 2006 Bessel pro

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https://doi.org/10.1007/978-3-319-17263-7It is well known that the random occupation measure induced by the sample path of a Brownian motion . = (., . ≥ 0) admits a jointly continuous local time process (L. (.); . ∈ ℝ, . ≥ 0) such that

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Coagulation and fragmentation processes,The work of Kingman and others shows how the theory of exchangeable random partitions and associated random discrete distributions provides a natural mathematical framework for the analysis of coagulation processes (also called coalescents) and fragmentation processes.

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Brownian local times, branching and Bessel processes,It is well known that the random occupation measure induced by the sample path of a Brownian motion . = (., . ≥ 0) admits a jointly continuous local time process (L. (.); . ∈ ℝ, . ≥ 0) such that

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Sequential constructions of random partitions,] which are consistent in a certain sense as . varies. This leads to consideration of a particular two-parameter family of exchangeable random partition structures, which can be characterized in various ways, and which is closely related to gamma and stable subordinators.

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Hikaru Kishimoto,Naoto Yanai,Shingo Okamura] which are consistent in a certain sense as . varies. This leads to consideration of a particular two-parameter family of exchangeable random partition structures, which can be characterized in various ways, and which is closely related to gamma and stable subordinators.

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