## Taiwanese Journal of Mathematics

### An Analytic Version of Wiener-Itô Decomposition on Abstract Wiener Spaces

#### Abstract

In this paper, we first establish an analogue of Wiener-Itô theorem on finite-dimensional Gaussian spaces through the inverse $S$-transform, that is, the Gauss transform on Segal-Bargmann spaces. Based on this point of view, on infinite-dimensional abstract Wiener space $(H,B)$, we apply the analyticity of the $S$-transform, which is an isometry from the $L^2$-space onto the Bargmann-Segal-Dwyer space, to study the regularity. Then, by defining the Gauss transform on Bargmann-Segal-Dwyer space and showing the relationship with the $S$-transform, an analytic version of Wiener-Itô decomposition will be obtained.

#### Article information

Source
Taiwanese J. Math., Volume 23, Number 2 (2019), 453-471.

Dates
Accepted: 10 December 2018
First available in Project Euclid: 28 December 2018

https://projecteuclid.org/euclid.twjm/1545966024

Digital Object Identifier
doi:10.11650/tjm/181207

Mathematical Reviews number (MathSciNet)
MR3936008

#### Citation

Lee, Yuh-Jia; Shih, Hsin-Hung. An Analytic Version of Wiener-Itô Decomposition on Abstract Wiener Spaces. Taiwanese J. Math. 23 (2019), no. 2, 453--471. doi:10.11650/tjm/181207. https://projecteuclid.org/euclid.twjm/1545966024

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