  We study orbital functions associated to finitely generated geometrically
infinite Kleinian groups acting on the hyperbolic space $\mathbb{H}^3$,
developing a new method based on the use of the Brownian motion. On the way, we
give some estimates of the orbital function associated to nilpotent covers of
compact hyperbolic manifolds, partially answering a question asked by M.
Pollicott to the author.
