Generalized multiple Wiener integrals

Abstract

1. Introduction.The analysis of nonlinear functionals of Brownian motion (B($)), which we call simply Brownian functionals, can be expressed in terms of white noise {/(t)), B(t)--dB(t)/dt.We are specifically interested in the so-called causal calculus where the propagation of time is taken into account.Intuitively speaking, may be taken to be a coordinate system of the basic space on which Brownian functionals are defined.At the same time, (/()} could be thought of as a system of variables of Brownin functionals.With this system the passage of time, say by h, can be represented explicitly as (t)-.(t+ h).In order to carry out the causal calculus we have naturally been led to the concept of generalized Brownian functionals ([3]).There we were inspired by P. L6vy's work [1] on functional analysis.

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