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An analog computer is used to apply a Monte Carlo method of solution to the parabolic partial differential equations that arise in stochastic time-optimal control theory. Using this method, an iterative technique called approximation-in-policy-space is applied to find the optimum switching curve. An example of a second-order inertial plant is considered, and the results are found to agree with those found by a perturbation given by Dorato et al. .