# A growth-fragmentation model related to Ornstein-Uhlenbeck type processes

## TL;DR

This paper introduces a new growth-fragmentation model linked to Lévy-driven Ornstein-Uhlenbeck processes, generalizing previous models and establishing convergence and law of large numbers.

## Contribution

It presents a novel growth-fragmentation framework related to Ornstein-Uhlenbeck processes, extending prior models and providing convergence and probabilistic laws.

## Key findings

- Established a convergence criterion for the new growth-fragmentation models.
- Proved a law of large numbers under certain conditions.
- Generalized compensated fragmentation processes.

## 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 L\'evy 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.