  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.
