Innovations for random fields

There is a famous formula called Levy's stochastic infinitesimal equation for a stochastic process X(t) expressed in the form delta X(t) = Phi (X(s),s less than or equal to t,Y-t, t, dt), t is an element of R-1. We propose a generalization of this equation for a random field X(C) indexed by a contour C. Assume that the X(C) is homogeneous in a white noise x, say of degree n, we can then appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X(C) and hence its probabilistic structure. Some of future directions are also mentioned.