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

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 analyticit...

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Bibliographic Details
Published in:Taiwanese journal of mathematics 2019-04, Vol.23 (2), p.453-471
Main Authors: Lee, Yuh-Jia, Shih, Hsin-Hung
Format: Article
Language:English
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Summary: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 L²-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.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm/181207