  This work concerns continuous-time, continuous-space stochastic dynamical
systems described by stochastic differential equations (SDE). It presents a new
approach to compute probabilistic safety regions, namely sets of initial
conditions of the SDE associated to trajectories that are safe with a
probability larger than a given threshold. The approach introduces a functional
that is minimised at the border of the probabilistic safety region, then solves
an optimisation problem using techniques from Malliavin Calculus, which
computes such region. Unlike existing results in the literature, the new
approach allows one to compute probabilistic safety regions without gridding
the state space of the SDE.
