An extension of the Cameron–Martin translation theorem via Fourier–Hermite functionals

In this paper, we use the Fourier–Hermite functionals to extend the structure of the Cameron–Martin translation theorem on an abstract Wiener space ( H , B , ν ) . The directional function in our translation theorem may not be in the Cameron–Martin subspace H of B . We then proceed to obtain an expl...

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Bibliographic Details
Published in:Archiv der Mathematik 2020-12, Vol.115 (6), p.679-689
Main Authors: Lee, Un Gi, Choi, Jae Gil
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this paper, we use the Fourier–Hermite functionals to extend the structure of the Cameron–Martin translation theorem on an abstract Wiener space ( H , B , ν ) . The directional function in our translation theorem may not be in the Cameron–Martin subspace H of B . We then proceed to obtain an explicit formula for our general translation theorem.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-020-01524-6