Stochastic approach of fragmentation – Application to avalanches – Madalina Deaconu

The aim of this talk is to introduce a numerical probabilis- tic approach for an avalanche-type process. The originality of our approach is to use a fragmentation model to describe the avalanche phenomenon. We start by introducing a new interpretation of the fragmentation equation by means of branching processes. A particular fragmentation kernel, which is discontinuous, leads to a stochastic model for the fragmentation phase of an avalanche. For these processes, solutions of some particular stochastic differential equa- tions of fragmentation, we construct a numerical approx- imation scheme. We analyse in particular this numerical results on our model of avalanches and emphasize the frac- tal property observed theoretically in our model. This is a joint work with Lucian Beznea (IMAR, Bucharest) and Oana Lupa ̧scu (IMAR, Bucharest).