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Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

Madalina Deaconu 1, 2 Nicolas Fournier 2 Etienne Tanré 3
1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
2 IECN - Institut Élie Cartan de Nancy
3 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).
Keywords : interacting stochastic particle systems Monte Carlo methods central limit theorem Smoluchowski coagulation equation
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https://hal.inria.fr/hal-01080453
Contributor : Etienne Tanré <>
Submitted on : Thursday, November 13, 2014 - 10:33:32 AM
Last modification on : Tuesday, May 18, 2021 - 2:32:03 PM

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Madalina Deaconu, Nicolas Fournier, Etienne Tanré. Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation. Methodology and Computing in Applied Probability, Springer Verlag, 2003, 5 (2), pp.131-158. ⟨10.1023/A:1024524500111⟩. ⟨hal-01080453⟩

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