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

Author

Listed:
  • Madalina Deaconu

    (IECN—INRIA Lorraine)

  • Nicolas Fournier

    (IECN)

  • Etienne Tanré

    (INRIA Sophia-Antipolis)

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).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:5:y:2003:i:2:d:10.1023_a:1024524500111
    DOI: 10.1023/A:1024524500111
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    Cited by:

    1. 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.
    2. Beznea, Lucian & Deaconu, Madalina & Lupaşcu-Stamate, Oana, 2019. "Numerical approach for stochastic differential equations of fragmentation; application to avalanches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 111-125.

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