Stochastic accessibility on Grushin-type manifolds

We consider a non-smooth Grushin-type distribution, defined on Rn, whose stochastic perturbation defines the admissible stochastic processes. Our main result is a stochastic accessibility theorem on the corresponding Grushin manifold. More specifically, given two points P and Q, we show how to steer an admissible stochastic processes, starting at P, such that it strikes an arbitrarily small ball centered at Q, asymptotically almost surely.