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Stochastic equation of fragmentation and branching processes related to avalanches

Lucian Beznea 1 Madalina Deaconu 2, 3 Oana Lupascu 2, 1, 3 
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
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. Stochastic equation of fragmentation and branching processes related to avalanches. Journal of Statistical Physics, Springer Verlag, 2016, 162 (4), pp.824-841. ⟨10.1007/s10955-015-1432-5⟩. ⟨hal-01216137⟩



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