The Annals of Applied Probability

Stochastic Particle Approximations for Smoluchoski’s Coagualtion Equation

Andreas Eibeck and Wolfgang Wagner

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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.

Article information

Source
Ann. Appl. Probab., Volume 11, Number 4 (2001), 1137-1165.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1015345398

Digital Object Identifier
doi:10.1214/aoap/1015345398

Mathematical Reviews number (MathSciNet)
MR1878293

Zentralblatt MATH identifier
1021.60086

Subjects
Primary: 60K40: Other physical applications of random processes 65C35: Stochastic particle methods [See also 82C80]

Keywords
Stochastic particle method coagulation equation variance reduction gelation phenomena

Citation

Eibeck, Andreas; Wagner, Wolfgang. Stochastic Particle Approximations for Smoluchoski’s Coagualtion Equation. Ann. Appl. Probab. 11 (2001), no. 4, 1137--1165. doi:10.1214/aoap/1015345398. https://projecteuclid.org/euclid.aoap/1015345398


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