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 continuous functions. The white noise commutation relations involve specially defined split delta functions rather than Dirac delta functions. This is vital to establish the commutativity of the Ito noise with adapted processes. The Stratonovich white noise is introduced inside the same framework.
|Translated title of the contribution||A new approach to non-commutative white noise analysis|
|Number of pages||5|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|Publication status||Published - Apr 1998|