Probabilistic numerical approximation for stochastic control problems

We give a probabilistic interpretation of the Monte-Carlo scheme proposed by Fahim, Touzi and Warin for fully nonlinear parabolic PDEs, and hence generalize it to the non-Markovian case for a general stochastic control problem. General convergence result is obtained by weak convergence method as in Kushner. We also get a rate of convergence using the invariance principle technique as in Dolinsky's work, which is better than that obtained by viscosity solution method.