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On long time behavior of some coagulation processes

Author

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  • Fournier, Nicolas
  • Roynette, Bernard
  • Tanré, Etienne

Abstract

We consider an infinite system of particles characterized by their position and mass, in which coalescence occurs. Each particle endures Brownian excitation, and is subjected to the attraction of a potential. We define a stochastic process (Xt,Mt)t[greater-or-equal, slanted]0 describing the evolution of the position and mass of a typical particle. We show that under some conditions, the mass process Mt tends almost surely to infinity, while the position process Xt tends almost surely to 0, as time tends to infinity.

Suggested Citation

  • Fournier, Nicolas & Roynette, Bernard & Tanré, Etienne, 2004. "On long time behavior of some coagulation processes," Stochastic Processes and their Applications, Elsevier, vol. 110(1), pages 1-17, March.
    • Handle: RePEc:eee:spapps:v:110:y:2004:i:1:p:1-17
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    References listed on IDEAS

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    1. Deaconu, Madalina & Fournier, Nicolas, 2002. "Probabilistic approach of some discrete and continuous coagulation equations with diffusion," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 83-111, September.
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