The Annals of Applied Probability

Stochastic Particle Approximations for Smoluchoski’s Coagualtion Equation

Andreas Eibeck and Wolfgang Wagner

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

First available in Project Euclid: 5 March 2002

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

Stochastic particle method coagulation equation variance reduction gelation phenomena


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.

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