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Analytic Functions on Abstract Wiener Spaces

✍ Scribed by Setsuo Taniguchi

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 181 KB
Volume: 179
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3676

No coin nor oath required. For personal study only.

✦ Synopsis

dedicated to professor d. w. stroock on his 60th birthday Let (X, H, +) be a real abstract Wiener space. A new definition of analytic functions on X is introduced, and it is shown that stochastic line integrals of real analytic 1-forms along Brownian motion and solutions to stochastic differential equations with real analytic coefficients are analytic Wiener functionals. An L p -theoretical sufficient condition for Wiener functionals to be analytic and an associated Cauchy formula are also established.

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