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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978-3-540-30990-1Springer-Verlag Berlin Heidelberg 2006

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An Overview of Future Microgrids, objects of considerable interest in probability theory. We may consider a random walk as a probability measure on sequences of steps-that is, on “walks”. A branching process is a probability measure on “trees”. The purpose of the present section is to show that walks and trees are abstractly identi

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Matthias Wagner,Paul Holleis,Hendrik Berndt various functionals of a uniformly distributed random mapping from an n element set to itself, are those of corresponding functionals of a Brownian bridge. Similar results known to hold for various non-uniform models of random mappings, according to a kind of invariance principle. A mapping . : [n]

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Anwendungssicht mobiler Geschäftsanwendungenbe constructed from random trees and forests. These constructions establish deep connections between the asymptotic behaviour of additive coalescent processes and the theory of Brownian trees and excursions. There are some close parallels with the theory of multiplicative coalescents and the asympto

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Prabh Bedi,Neha Goel Tripathi,H. B. SinghThis chapter provides an introduction to the elementary theory of Bell polynomials and their applications in probability and combinatorics.

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https://doi.org/10.1007/978-3-030-02656-1The 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.