Ideal and physical white noise in stochastic analysis

Abstract

The concept of ideal white noise and the subsequent Itô and Stratonovich integral concepts seem to be useful only for mathematical manipulation in deriving the moment equations for non-linear systems under parametric white noise. For physical white noise, that is for a band limited white noise, the two integrals coincide. This paper is devoted to a further insight into this problem starting from a single deterministic parametric impulse showing that a difference between physical and ideal white noise is only related to different forms of integration of the Dirac delta occurrence.