A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space
We shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/1/12 |
| _version_ | 1797543791563898880 |
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| author | Young Sik Kim |
| author_facet | Young Sik Kim |
| author_sort | Young Sik Kim |
| collection | DOAJ |
| description | We shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we obtain those relationships in the Fresnel class as it’s corollaries. |
| first_indexed | 2024-03-10T13:50:37Z |
| format | Article |
| id | doaj.art-b153f1bbedc4471995ac31ddebd1ab0b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T13:50:37Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b153f1bbedc4471995ac31ddebd1ab0b2023-11-21T02:12:52ZengMDPI AGSymmetry2073-89942020-12-011311210.3390/sym13010012A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener SpaceYoung Sik Kim0Department of Mathematics, College of Natural Sciences, Industry-University Cooperation Foundation, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, KoreaWe shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we obtain those relationships in the Fresnel class as it’s corollaries.https://www.mdpi.com/2073-8994/13/1/12abstract Wiener spaceFourier–Feynman transformchange of scale formula |
| spellingShingle | Young Sik Kim A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space Symmetry abstract Wiener space Fourier–Feynman transform change of scale formula |
| title | A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space |
| title_full | A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space |
| title_fullStr | A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space |
| title_full_unstemmed | A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space |
| title_short | A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space |
| title_sort | change of scale formula for wiener integrals about the first variation on the product abstract wiener space |
| topic | abstract Wiener space Fourier–Feynman transform change of scale formula |
| url | https://www.mdpi.com/2073-8994/13/1/12 |
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