  In this note, we consider general growth-fragmentation equations from a
probabilistic point of view. Using Foster-Lyapunov techniques, we study the
recurrence of the associated Markov process depending on the growth and
fragmentation rates. We prove the existence and uniqueness of its stationary
distribution, and we are able to derive precise bounds for its tails in the
neighborhoods of both $0$ and $+\infty$. This study is systematically compared
to the results obtained so far in the literature for this class of
integro-differential equations.
