Mădălina Deaconu
Inria Nancy - Grand Est & IECL, Nancy, France

Stochastic modeling is a fundamental tool in understanding, describing, predicting and even generalizing complex phenomena. We develop in this talk fragmentation models which are used in many applications such as: in chemistry, the formation of polymers; in astrophysics, the formation of stars and planets; in geophysics, the formation of fractures or earthquakes, etc. The equation represents the evolution of the concentration of mass of particles which undergo fragmentation in time. We present here an overview of a large class of probabilistic representations of the fragmentation equation, and we develop and study the interconnections in between these representations. These probabilistic tools range from Markov chains to stochastic differential equations with jumps The mathematical difficulties are numerous and we underline the advantage of the probabilistic interpretation in this context. An important feature of these stochastic models is given by the construction of simple numerical method, allowing to describe the behaviour of the mass of the particles over time. This is a common work with Antoine Lejay (Inria Nancy - Grand Est & Institut Élie Cartan de Lorraine).