Article
| Title: | Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space (English) |
| Author: | Choi, Jae Gil |
| Author: | Shim, Sang Kil |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 849-868 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space $(H,B,\nu )$. An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space $B$. Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur and Bromley Fresnel class $\mathcal F(B)$ and we finally investigate some Fubini theorems involving CFFT. (English) |
| Keyword: | abstract Wiener space |
| Keyword: | conditional Wiener integral |
| Keyword: | conditional Fourier-Feynman transform |
| Keyword: | Fubini theorem |
| MSC: | 28C20 |
| MSC: | 42B10 |
| MSC: | 46B09 |
| MSC: | 46G12 |
| idZBL: | Zbl 07729541 |
| idMR: | MR4632861 |
| DOI: | 10.21136/CMJ.2023.0310-22 |
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| Date available: | 2023-08-11T14:25:55Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151778 |
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