where t e R is the time, x ~ R" is the state variable, u = u(t) ~ R p and v = v(t) ~ R q are control variables and w = w(t, ~o)~ R" is some stochastic process defined over the probability space (f2, 0, t0, where f~ is a nonempty abstract set, 0 is a o-algebra of subsets of f2 and tz is a probability measure on 0. In this game, one player, called u, controls the function u(t) and another player, called v, controls the function v(t). Let the initial state of the game be given by Xo = x(to) and the terminal condition by the expression