A growth-fragmentation model related to Ornstein-Uhlenbeck type processes
arXiv:1702.01091 · doi:10.1214/19-AIHP974
Abstract
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 Lévy driven Ornstein-Uhlenbeck type processes. Our model can be viewed as a generalization of compensated fragmentation processes introduced by Bertoin, or the stochastic counterpart of a family of growth-fragmentation equations. We establish a convergence criterion for a sequence of such growth-fragmentations. We also prove that, under certain conditions, this system fulfills a law of large numbers.
34 pages, to appear in Annales de l'Institut Henri Poincaré
References in corpus (8)
- Ranked Fragmentations
- A probabilistic approach to spectral analysis of growth-fragmentation equations
- Discretization methods for homogeneous fragmentations
- Asymptotics of self-similar growth-fragmentation processes
- The fragmentation process of an infinite recursive tree and Ornstein-Uhlenbeck type processes
- The Mittag-Leffler process and a scaling limit for the block counting process of the Bolthausen-Sznitman coalescent
- Infinitely ramified point measures and branching Lévy processes
- Probability tilting of compensated fragmentations