A NEW APPROACH TO NONCOMMUTATIVE WHITE-NOISE ANALYSIS

A theory of distributions over piecewise continuous test functions is introduced and used as the basis for the construction of a new theory of white noise analysis on the Fock space of multivariate piecewise co ntinuous functions. The white noise commutation relations involve spec ially defined split delta functions rather than Dirac delta functions. This is vital to establish the commutativity of the Ito noise with ad apted processes. The Stratonovich white noise is introduced inside the same framework. (C) Academie des Sciences/Elsevier, Paris.