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Smoluchowski's equation: Rate of convergence of the Marcus-Lushnikov process

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  • Cepeda, Eduardo
  • Fournier, Nicolas

Abstract

We derive a satisfying rate of convergence of the Marcus-Lushnikov process towards the solution to Smoluchowski's coagulation equation. Our result applies to a class of homogeneous-like coagulation kernels with homogeneity degree ranging in (-[infinity],1]. It relies on the use of a Wasserstein-type distance, which has shown to be particularly well-adapted to coalescence phenomena. It was introduced and used in preceding works (Fournier and Laurençot (2006) [7]) and (Fournier and Löcherbach (2009) [8]).

Suggested Citation

  • Cepeda, Eduardo & Fournier, Nicolas, 2011. "Smoluchowski's equation: Rate of convergence of the Marcus-Lushnikov process," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1411-1444, June.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:6:p:1411-1444
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    References listed on IDEAS

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    1. Madalina Deaconu & Nicolas Fournier & Etienne Tanré, 2003. "Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation," Methodology and Computing in Applied Probability, Springer, vol. 5(2), pages 131-158, June.
    2. Fournier, Nicolas & Löcherbach, Eva, 2009. "Stochastic coalescence with homogeneous-like interaction rates," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 45-73, January.
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    Cited by:

    1. Cepeda, Eduardo, 2016. "Stochastic coalescence multi-fragmentation processes," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 360-391.
    2. Vassili Kolokoltsov & Marianna Troeva & Wei Yang, 2014. "On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players," Dynamic Games and Applications, Springer, vol. 4(2), pages 208-230, June.

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