Scaling property for fragmentation processes related to avalanches

Lucian Beznea (1, 2) , Madalina Deaconu (3, 4, 5) , Oana Lupaşcu-Stamate (6)

1 IMAR - "Simion Stoilow" Institute of Mathematics
2 UniBuc - University of Bucharest
3 IECL - Institut Élie Cartan de Lorraine
4 PASTA - Processus aléatoires spatio-temporels et leurs applications
5 TOSCA-NGE-POST - Simuler et calibrer des modèles stochastiques
6 Romanian Academy

We emphasize a scaling property for the continuous time fragmentation processes related to a stochastic model for the fragmentation phase of an avalanche. We present numerical results that confirm the validity of the scaling property for our model, based on the appropriate stochastic differential equation of fragmentation and on a fractal property of the solution.

Mots clés: scaling; fragmentation stochastic differential equation; jump process; Monte Carlo method

Domaines: Probabilités [math.PR]

Lucian Beznea, Madalina Deaconu, Oana Lupaşcu-Stamate. Scaling property for fragmentation processes related to avalanches. Applications of Mathematics and Informatics in Natural Sciences and Engineering, Applications of Mathematics and Informatics in Natural Sciences and Engineering AMINSE 2019, Tbilisi, Georgia, September 23–26 (334), Springer, 2021, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-030-56356-1_3⟩. ⟨hal-02942710⟩