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

Lucian Beznea, Madalina Deaconu and Oana Lupaşcu-Stamate

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 160, issue C, 111-125

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.

Keywords: Fragmentation equation and kernel; Avalanche; Branching process and kernel; Stochastic equation of fragmentation; Numerical methods (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:160:y:2019:i:c:p:111-125

DOI: 10.1016/j.matcom.2018.12.004

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