Stochastic equation of fragmentation and branching processes related to avalanches

TL;DR

This paper introduces a stochastic model for snow avalanche fragmentation, using a fragmentation-branching process and a stochastic equation, highlighting fractal properties and employing probabilistic and analytic methods.

Contribution

It develops a novel stochastic fragmentation-branching process model for avalanches, incorporating fractal properties and a specific stochastic equation of fragmentation.

Findings

Fractal property of the fragmentation-branching process

Construction of a stochastic equation for fragmentation

Use of branching Markov processes for continuous evolution

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.