Oana Lupaşcu-Stamate
Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania

We develop the study of a binary coagulation-fragmentation equation which describes the avalanches phenomena. We construct first an adapted stochastic process and obtain its behaviourto the equilibrium. Our model is based on self-organized critical (SOC) systems and in partic-ular on a simple sand pile model introduced in Bressaud and Fournier.

Furthermore, we definea stochastic differential equation for this process and propose a numerical method in order to approximate the solution. The key point of our work is a new interpretation of the avalanches phenomena by handling stochastic differential equations with jumps and the analysis of the invariant behaviour of the stochastic process.

The results are obtained jointly with Madalina Deaconu (Nancy).