A Review of White Noise Analysis from a Probabilistic Standpoint

摘要

The main notions and tools from white noise analysis are set up on the basis of the calculus of Gaussian random variables and the S -transform. A new proof of the formula for the S -transform of It? integrals is given. Moreover, measurability and the martingale property with respect to the Brownian filtration are characterized in terms of the S-transform. This allows the extension of these notions to random variables and processes, respectively, in the space of Hida distributions.