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May 2002 Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations
Jean Bertoin
Ann. Appl. Probab. 12(2): 547-564 (May 2002). DOI: 10.1214/aoap/1026915615

Abstract

The cornerstone of this work, which is partly motivated by the characterization of the so-called eternal additive coalescents by Aldous and Pitman, is an explicit expression for the general eternal solution to Smoluchowski's coagulation equation with additive kernel. This expression points at certain Lévy processes with no negative jumps and more precisely at a stochastic model for aggregation based on such processes, which has been recently considered by Bertoin and Miermont and is known to bear close relations with the additive coalescence. As an application, we show that the eternal solutions can be obtained from some hydrodynamic limit of the stochastic model. We also present a simple condition that ensures the existence of a smooth density for an eternal solution.

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Jean Bertoin. "Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations." Ann. Appl. Probab. 12 (2) 547 - 564, May 2002. https://doi.org/10.1214/aoap/1026915615

Information

Published: May 2002
First available in Project Euclid: 17 July 2002

zbMATH: 1030.60036
MathSciNet: MR1910639
Digital Object Identifier: 10.1214/aoap/1026915615

Subjects:
Primary: 60G51, 60K35, 82C21

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 2 • May 2002
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