Some Fundamental Formulas for an Integration on Infinite Dimensional Hilbert Spaces

Chung, Hyun Soo

doi:10.1007/s11785-022-01302-y

Search citation statements

Order By: Relevance

Paper Sections

Select...

Definitions and Preliminaries1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(iv) The ⟨v, x⟩ is a Gaussian random variable with mean 0 and variance ∥v∥ 2 2 . For a more detailed study of the PWZ stochastic integral, see [2,6,8,[13][14][15][16][17]. We are ready to recall the definitions of analytic Feynman integral and analytic FFT on Wiener space [1][2][3].…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

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

Chung

2024

Axioms

Self Cite

View full text Add to dashboard Cite

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.

show abstract