6533b854fe1ef96bd12ae14a

RESEARCH PRODUCT

A Path-Integral Approach to the Cameron-Martin-Maruyama-Girsanov Formula Associated to a Bilaplacian

Rémi Léandre

subject

Pure mathematicsGirsanov theoremArticle SubjectSemigroupMathematics::Operator Algebraslcsh:MathematicsSpace (mathematics)lcsh:QA1-939AlgebraDistribution (mathematics)Product (mathematics)Path integral formulationPath spaceAnalysisMathematics

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.

yearjournalcountryeditionlanguage
2012-01-01Journal of Function Spaces and Applications
10.1155/2012/458738https://doaj.org/article/bd16a23b6900491a85bcd9a7349ba3dc