Wiener Distributions and White Noise Analysis

Authors

David E. Betounes, University of Southern MississippiFollow
Mylan Redfern, University of Southern MississippiFollow

Document Type

Article

Publication Date

7-1-1992

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

The paper describes the structure of a new space of generalized Wiener functionals, (D_∞)^*, 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 θ:R^N→(D_∞)^* are introduced, and a derivative version of Itô's lemma is proved. The algebraic structure of (D_∞)^* 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

Recommended Citation

Betounes, D. E., Redfern, M. (1992). Wiener Distributions and White Noise Analysis. Applied Mathematics and Optimization, 26(1), 63-93.
Available at: https://aquila.usm.edu/fac_pubs/6792