A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian
We define the Wiener product on a bosonic Connes space associated to a Bilaplacian and we introduce formal Wiener chaos on the path space. We consider the vacuum distribution on the bosonic Connes space and show that it is related to the heat semigroup associated to the Bilaplacian. We deduce a Came...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/458738 |
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| _version_ | 1850177852394176512 |
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| author | Rémi Léandre |
| author_facet | Rémi Léandre |
| author_sort | Rémi Léandre |
| collection | DOAJ |
| description | We define the Wiener product on a bosonic Connes space associated to a Bilaplacian and we introduce formal Wiener chaos on the path space. We consider the vacuum distribution on the bosonic Connes space and show that it is related to the heat semigroup associated to the Bilaplacian. We deduce a Cameron-Martin quasi-invariance formula for the heat semigroup associated to the Bilaplacian by using some convenient coherent vector. This paper enters under the Hida-Streit approach of path integral. |
| format | Article |
| id | doaj-art-bd16a23b6900491a85bcd9a7349ba3dc |
| institution | OA Journals |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-bd16a23b6900491a85bcd9a7349ba3dc2025-08-20T02:18:54ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/458738458738A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a BilaplacianRémi Léandre0Institut de Mathématiques, Université de Bourgogne, 21000 Dijon, FranceWe define the Wiener product on a bosonic Connes space associated to a Bilaplacian and we introduce formal Wiener chaos on the path space. We consider the vacuum distribution on the bosonic Connes space and show that it is related to the heat semigroup associated to the Bilaplacian. We deduce a Cameron-Martin quasi-invariance formula for the heat semigroup associated to the Bilaplacian by using some convenient coherent vector. This paper enters under the Hida-Streit approach of path integral.http://dx.doi.org/10.1155/2012/458738 |
| spellingShingle | Rémi Léandre A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian Journal of Function Spaces and Applications |
| title | A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian |
| title_full | A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian |
| title_fullStr | A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian |
| title_full_unstemmed | A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian |
| title_short | A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian |
| title_sort | path integral approach to the cameron martin maruyama girsanov formula associated to a bilaplacian |
| url | http://dx.doi.org/10.1155/2012/458738 |
| work_keys_str_mv | AT remileandre apathintegralapproachtothecameronmartinmaruyamagirsanovformulaassociatedtoabilaplacian AT remileandre pathintegralapproachtothecameronmartinmaruyamagirsanovformulaassociatedtoabilaplacian |