The deterministic stochastic transition in control processes and the use of maximum and integral transforms

that is, F is the "maximum transform" of b. We shall refer to transforms of either type generically as "maximum transforms." In this paper we shall show that use of the transform leads to a very natural treatment of certain control problems. The pair of relations (1.1), (1.2) is strikingly analogous in form to a Fourier integral transformation and its inversion. The analogy is more than fortuitous. Consider a pair of functions F, ci, linked via the reciprocal Fourier relations