  In this paper, stochastic optimal control problems in continuous time and
space are considered. In recent years, such problems have received renewed
attention from the lens of reinforcement learning (RL) which is also one of our
motivation. The main contribution is a simulation-based algorithm -- dual
ensemble Kalman filter (EnKF) -- to numerically approximate the solution of
these problems. The paper extends our previous work where the dual EnKF was
applied in deterministic settings of the problem. The theoretical results and
algorithms are illustrated with numerical experiments.
