Ornstein-Uhlenbeck type growth-fragmentation processes

par Quan Shi (Paris 13)

jeudi 16 mars 2017, 14:30 → 15:30 Europe/Paris

salle 435 (UMPA)

Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we introduce a new type of growth-fragmentation which is closely related to L\'evy driven Ornstein-Uhlenbeck type processes. Our model can be viewed as a generalization of compensated fragmentation processes introduced by Bertoin (Ann. Probab. 2016). We establish a convergence criterion for a sequence of such growth-fragmentations. We also prove that, under certain conditions, the average size of the particles converges to a stationary distribution as time tends to infinity.