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Numerical approach for stochastic differential equations of fragmentation; application to avalanches

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  • Beznea, Lucian
  • Deaconu, Madalina
  • Lupaşcu-Stamate, Oana

Abstract

We build and develop a unifying method for the construction of a continuous time branching–fragmentation processes on the space of all fragmentation sizes, induced either by continuous fragmentation kernels or by discontinuous ones. This construction leads to a stochastic model for the fragmentation phase of an avalanche. We introduce an approximation scheme for the process which solves the corresponding stochastic differential equations of fragmentation. One of the main achievements of the paper is to compute the distributions of the branching processes approximating the forthcoming branching–fragmentation process. Finally, we present numerical results that confirm the validity of the fractal property which was emphasized by our model for an avalanche.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:160:y:2019:i:c:p:111-125
    DOI: 10.1016/j.matcom.2018.12.004
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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. Beznea, Lucian & Deaconu, Madalina & Lupaşcu, Oana, 2015. "Branching processes for the fragmentation equation," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1861-1885.
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