  We propose a new probabilistic numerical scheme for fully nonlinear equation
of Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem,
which is based on the Feynman-Kac representation in [12] by means of control
randomization and backward stochastic differential equation with nonpositive
jumps. We study a discrete time approximation for the minimal solution to this
class of BSDE when the time step goes to zero, which provides both an
approximation for the value function and for an optimal control in feedback
form. We obtained a convergence rate without any ellipticity condition on the
controlled diffusion coefficient. Explicit implementable scheme based on
Monte-Carlo simulations and empirical regressions, associated error analysis,
and numerical experiments are performed in the companion paper [13].
