  We tackle a nonlinear optimal control problem for a stochastic differential
equation in Euclidean space and its state-linear counterpart for the
Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach
is founded on a novel concept of local optimality surpassing Pontryagin's
minimum, originally crafted for deterministic optimal ensemble control
problems. A key practical outcome is a rapidly converging numerical algorithm,
which proves its feasibility for problems involving Markovian and open-loop
strategies.
