Open Access
April, 2019 An Analytic Version of Wiener-Itô Decomposition on Abstract Wiener Spaces
Yuh-Jia Lee, Hsin-Hung Shih
Taiwanese J. Math. 23(2): 453-471 (April, 2019). DOI: 10.11650/tjm/181207


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.


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Yuh-Jia Lee. Hsin-Hung Shih. "An Analytic Version of Wiener-Itô Decomposition on Abstract Wiener Spaces." Taiwanese J. Math. 23 (2) 453 - 471, April, 2019.


Received: 8 May 2018; Accepted: 10 December 2018; Published: April, 2019
First available in Project Euclid: 28 December 2018

zbMATH: 07055577
MathSciNet: MR3936008
Digital Object Identifier: 10.11650/tjm/181207

Primary: ‎46E20‎ , 46E50 , 60B11
Secondary: 28C20

Keywords: abstract wiener measure , Abstract Wiener space , Gauss transform , Segal-Bargmann transform , Wiener-Itô decomposition

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

Vol.23 • No. 2 • April, 2019
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