Grid-Free Computation of Probabilistic Safety with Malliavin Calculus

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