Title

Wiener Distributions and White Noise Analysis

Document Type

Article

Publication Date

7-1-1992

Department

Mathematics

Abstract

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.

Publication Title

Applied Mathematics and Optimization

Volume

26

Issue

1

First Page

63

Last Page

93