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- Title
The behavior of conditional Wiener integrals on product Wiener space.
- Authors
Choi, Jae Gil; Skouge, David; Chang, Seung Jun
- Abstract
In this paper we first investigate the behavior of conditional Wiener integrals on product Wiener spaces and then proceed to establish a Fubini theorem for conditional Wiener integrals. We then define a very general multiple conditional analytic Fourier-Feynman transform and a multiple conditional analytic convolution product for functionals on Wiener space and then establish a relationship between them. Next we obtain a basic formula for the conditional Wiener integral involving the first variation and the n-dimensional Wiener directional derivative. Finally we establish several evaluation formulas for conditional Wiener and Feynman integrals involving the n-dimensional Wiener directional derivative of functionals on Wiener space.
- Subjects
WIENER integrals; FOURIER transforms; MATHEMATICAL convolutions; INTEGERS; PROBABILITY theory
- Publication
Mathematische Nachrichten, 2013, Vol 286, Issue 11/12, p1114
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.201200221