Analytic functions on abstract Wiener spaces
type: Item
instance of: scholarly article
title: Analytic functions on abstract Wiener spaces
zbMATH Open document ID: 0969.60060
author: Setsuo Taniguchi
published in: Journal of Functional Analysis
publication date: 2001-09-23T00:00:00Z
review text: Let \((X,H,\mu)\) be a real abstract Wiener space. In former papers, \textit{P. Malliavan} and the author [C. R. Acad. Sci., Paris, Sér. I 322, No. 3, 261-265 (1996; Zbl 0860.60048) and J. Funct. Anal. 143, 470-528 (1997; Zbl 0873.60040)] introduced a concept of analytic functions on \(X\) and of their holomorphic prolongation. The aim of this paper is to introduce a new class of analytic functions, possessing random convergence radii. This new class turns out to be more general than the earlier one. The author proves a Cauchy formula for those functions and gives an \(L_p\)-sufficient condition for analyticity. As example, it is shown that certain stochastic line integrals as well as some solutions of stochastic differential equations are analytic Wiener functionals.
reviewed by: Werner Linde
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 1579766
zbMATH Keywords: stochastic line integral
zbMATH Keywords: stochastical differential equations
zbMATH Keywords: Malliavin calculus
MaRDI profile type: Publication
full work available at URL: jfan.2000.3676
OpenAlex ID: W2048759534
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DOI: 10.1006/JFAN.2000.3676
description: scientific article; zbMATH DE number 1579766