  We give a probabilistic interpretation of the Monte Carlo scheme proposed by
Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322-1364] for fully
nonlinear parabolic PDEs, and hence generalize it to the path-dependent (or
non-Markovian) case for a general stochastic control problem. A general
convergence result is obtained by a weak convergence method in the spirit of
Kushner and Dupuis [Numerical Methods for Stochastic Control Problems in
Continuous Time (1992) Springer]. We also get a rate of convergence using the
invariance principle technique as in Dolinsky [Electron. J. Probab. 17 (2012)
1-5], which is better than that obtained by viscosity solution method. Finally,
by approximating the conditional expectations arising in the numerical scheme
with simulation-regression method, we obtain an implementable scheme.
