Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations
type: Item
instance of: scholarly article
title: Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations
zbMATH Open document ID: 1030.60036
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: An explicit expression is obtained for the general eternal solution to Smoluchowski's equation with additive kernel. Probabilistic interpretation and some applications to Lévy processes are presented.
reviewed by: Nijolė Kalinauskaitė
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1906169
zbMATH Keywords: Smoluchowski's coagulation equation
zbMATH Keywords: additive coalesccence
zbMATH Keywords: Lévy processes
author: Jean Bertoin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1026915615
OpenAlex ID: W2046724876
cites work: Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
cites work: The standard additive coalescent
cites work: Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
cites work: Q4888858
cites work: Q4941947
cites work: A fragmentation process connected to Brownian motion
cites work: Eternal additive coalescents and certain bridges with exchangeable increments
cites work: Limit distributions and random trees derived from the birthday problem with unequal probabilities
cites work: Phase transition for Parking blocks, Brownian excursion and coalescence
cites work: A pure jump Markov process associated with Smoluchowski's coagulation equation
cites work: Q5696764
cites work: Construction of Markovian coalescents
cites work: Q4096243
cites work: The Limit of a Sequence of Branching Processes
cites work: Continuous state branching processes
cites work: On the Scalar Transport Equation
cites work: Ordered additive coalescent and fragmentations associated to Lévy processes with no positive jumps
cites work: Smoluchowski's coagulation equation: Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent
cites work: Q4937701
cites work: Applications of the continuous-time ballot theorem to Brownian motion and related processes.
DOI: 10.1214/AOAP/1026915615
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description: scientific article; zbMATH DE number 1906169