Wiener Distributions and White Noise Analysis
The paper describes the structure of a new space of generalized Wiener functionals, (D infinity)*, called the Wiener algebra, or space of Wiener distributions, and demonstrates its use in the white noise analysis. The concepts of derivatives and integrals for multi-time parameter generalized stochastic process theta: R(N) --> (D infinity)* are introduced, and a derivative version of Ito's lemma is proved. The algebraic structure of (D infinity)* and its lattice of subspaces is elaborated, and within this framework a generalized version of the Malliavin calculus is presented.
Applied Mathematics and Optimization
Betounes, D. E.,
(1992). Wiener Distributions and White Noise Analysis. Applied Mathematics and Optimization, 26(1), 63-93.
Available at: https://aquila.usm.edu/fac_pubs/6792