A Series Approximation for the Analytic Fourier–Feynman Transform on Wiener Space

In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out easy an calculation for the analytic Fourier–Feynman transform of the functionals. Some examples are furnished to illustrate the use...

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Bibliographic Details
Published in:Axioms 2024-04, Vol.13 (4), p.237
Main Author: Chung, Hyun Soo
Format: Article
Language:English
Subjects:
analytic Fourier–Feynman transform
Approximation
evaluation formula
Fourier transforms
Integrals
Mathematical analysis
Metric space
Numbers
Random variables
series approximation
unbounded functionals
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Summary:In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out easy an calculation for the analytic Fourier–Feynman transform of the functionals. Some examples are furnished to illustrate the usefulness of the evaluation formula. Finally, using the evaluation formula, we establish the series approximation for the analytic Fourier–Feynman transform.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13040237