Generalized Brownian Motion,Point Processes and Stochastic Calculus for Random Fields

A representation of the Malliavian derivative and the Skorochod integral in terms of random point systems on Polish spaces (and thus generalizing from the unit interval) is derived. This leads to a stochastic calculus based on random point systems. The operators are given explicitely and in a simple form allowing concrete probabilistic and quantum probabilistic interpretations.