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.
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