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November 2001 Stochastic Particle Approximations for Smoluchoski’s Coagualtion Equation
Andreas Eibeck, Wolfgang Wagner
Ann. Appl. Probab. 11(4): 1137-1165 (November 2001). DOI: 10.1214/aoap/1015345398

Abstract

This paper studies stochastic particle approximations for Smoluchowski’s coagulation equation. A new stochastic algorithm with reduced variance is proposed. Its convergence behavior is investigated, when the number of simulation particles tends to infinity. Under appropriate assumptions on the coagulation kernel, the limit is the unique solution of the coagulation equation. Then detailed numerical experiments are performed, testing the applicability and efficiency of the algorithm. In particular, the gelation phenomenon (loss of mass in the coagulation equation) is studied numerically for several kernels. A striking feature of the new algorithm is a better convergence after the gelation point, providing a tool for detecting the mass of the gel.

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Andreas Eibeck. Wolfgang Wagner. "Stochastic Particle Approximations for Smoluchoski’s Coagualtion Equation." Ann. Appl. Probab. 11 (4) 1137 - 1165, November 2001. https://doi.org/10.1214/aoap/1015345398

Information

Published: November 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1021.60086
MathSciNet: MR1878293
Digital Object Identifier: 10.1214/aoap/1015345398

Subjects:
Primary: 60K40 , 65C35

Keywords: coagulation equation , gelation phenomena , Stochastic particle method , variance reduction

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.11 • No. 4 • November 2001
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