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arXiv · 1508.00361

Stochastic equation of fragmentation and branching processes related to avalanches

Lucian Beznea·Madalina Deaconu·Oana Lupascu
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Abstract

We give a stochastic model for the fragmentation phase of a snow avalanche. We construct a fragmentation-branching process related to the avalanches, on the set of all fragmentation sizes introduced by J. Bertoin. A fractal property of this process is emphasized. We also establish a specific stochastic equation of fragmentation. It turns out that specific branching Markov processes on finite configurations of particles with sizes bigger than a strictly positive threshold are convenient for describing the continuous time evolution of the number of the resulting fragments. The results are obtained by combining analytic and probabilistic potential theoretical tools.

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Lucian Beznea, Madalina Deaconu, Oana Lupascu. 2015-08-03. Stochastic equation of fragmentation and branching processes related to avalanches. https://doi.org/10.1007/s10955-015-1432-5

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