Journal of the
Korean Mathematical Society JKMS

We apply the generalization of L\'evy's infinitesimal equation \begin{eqnarray*} \delta X(t)=\phi (X(s), s\leq t, Y_t,t,dt),\ t\in R^1, \end{eqnarray*} for a random field $X(C)$ indexed by a contour $C$ or by a more general set. Assume that the $X(C)$ is homogeneous in $x$, say of degree $n,$ then we can %%%homogeneous 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 $X(C.)$

Keywords: white noise, innovation, random field

MSC numbers: 60H30, 46G20