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Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations


Bertoin, Jean (2002). Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations. Annals of Applied Probability, 12(2):547-564.

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:
Language:English
Date:2002
Deposited On:03 Jul 2013 13:11
Last Modified:05 Apr 2016 16:51
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/aoap/1026915615
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1910639
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1030.60036

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