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August 2003 Stochastic interacting particle systems and nonlinear kinetic equations
Andreas Eibeck, Wolfgang Wagner
Ann. Appl. Probab. 13(3): 845-889 (August 2003). DOI: 10.1214/aoap/1060202829

Abstract

We present the stochastic approach to nonlinear kinetic equations (without gradient terms) in a unifying general framework, which covers many interactions important in applications, such as coagulation, fragmentation, inelastic collisions, as well as source and efflux terms. We provide conditions for the existence of corresponding stochastic particle systems in the sense of regularity (nonexplosion) of a jump process with unbounded intensity. Using an appropriate space of measure-valued functions, we prove relative compactness of the sequence of processes and characterize the weak limits in terms of solutions to the nonlinear equation. As a particular application, we derive existence theorems for Smoluchowski's coagulation equation with fragmentation, efflux and source terms, and for the Boltzmann equation with inelastic collisions.

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Andreas Eibeck. Wolfgang Wagner. "Stochastic interacting particle systems and nonlinear kinetic equations." Ann. Appl. Probab. 13 (3) 845 - 889, August 2003. https://doi.org/10.1214/aoap/1060202829

Information

Published: August 2003
First available in Project Euclid: 6 August 2003

zbMATH: 1045.60104
MathSciNet: MR1994039
Digital Object Identifier: 10.1214/aoap/1060202829

Subjects:
Primary: 60K40 , 65C35

Keywords: coagulation , dissipative collisions , existence of solutions , fragmentation , kinetic equations , regularity of jump processes , source and efflux , Stochastic particle systems

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 3 • August 2003
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