  We consider continuous state branching processes that are perturbed by a
Brownian motion. These processes are constructed as the unique strong solution
of a stochastic differential equation. The long-term extinction and explosion
behaviours are studied. In the stable case, the extinction and explosion
probabilities are given explicitly. We find three regimes for the asymptotic
behaviour of the explosion probability and, as in the case of branching
processes in random environment, we find five regimes for the asymptotic
behaviour of the extinction probability. In the supercritical regime, we study
the process conditioned on eventual extinction where three regimes for the
asymptotic behaviour of the extinction probability appear. Finally, the process
conditioned on non-extinction and the process with immigration are given.
