Abstract
Let (X, H, μ) 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 Lp-theoretical sufficient condition for Wiener functionals to be analytic and an associated Cauchy formula are also established.
Original language | English |
---|---|
Pages (from-to) | 235-250 |
Number of pages | 16 |
Journal | Journal of Functional Analysis |
Volume | 179 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 10 2001 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Analysis
Cite this
Analytic Functions on Abstract Wiener Spaces. / Taniguchi, Setsuo.
In: Journal of Functional Analysis, Vol. 179, No. 1, 10.01.2001, p. 235-250.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analytic Functions on Abstract Wiener Spaces
AU - Taniguchi, Setsuo
PY - 2001/1/10
Y1 - 2001/1/10
N2 - Let (X, H, μ) 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 Lp-theoretical sufficient condition for Wiener functionals to be analytic and an associated Cauchy formula are also established.
AB - Let (X, H, μ) 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 Lp-theoretical sufficient condition for Wiener functionals to be analytic and an associated Cauchy formula are also established.
UR - http://www.scopus.com/inward/record.url?scp=0043241680&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0043241680&partnerID=8YFLogxK
U2 - 10.1006/jfan.2000.3676
DO - 10.1006/jfan.2000.3676
M3 - Article
AN - SCOPUS:0043241680
VL - 179
SP - 235
EP - 250
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -