Translation Theorem for Function Space Integral Associated with Gaussian Paths and Applications

In this paper we establish a more general translation theorem for function space integral associated with Gaussian paths on the function space C a , b [ 0 , T ] . The function space C a , b [ 0 , T ] is induced by a generalized Brownian motion process. Thus, the Gaussian processes used in this paper...

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Bibliographic Details
Published in:Bulletin of the Iranian Mathematical Society 2019-10, Vol.45 (5), p.1367-1387
Main Authors: Chang, Seung Jun, Choi, Jae Gil
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Paper
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Summary:In this paper we establish a more general translation theorem for function space integral associated with Gaussian paths on the function space C a , b [ 0 , T ] . The function space C a , b [ 0 , T ] is induced by a generalized Brownian motion process. Thus, the Gaussian processes used in this paper are non-centered processes. We next apply our fundamental translation theorem to the generalized Fourier–Feynman transforms. We then proceed to show that these general translation theorems for the generalized Fourier–Feynman transforms can be applied to two well-known classes of functionals on the function space C a , b [ 0 , T ] .
ISSN:1017-060X
1735-8515
DOI:10.1007/s41980-018-00203-1