Evaluation Formula and Approximation for Wiener Integrals via the Fourier-Type Functional. (4th June 2021)

• Record Type: Journal Article
• Authors: Chung, Hyun Soo; Lee, Un Gi
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 5(2021)
• Page Start: 608
• Page End: 617
• Publication Date: 2021-06-04
• Subjects: Evaluation formula -- Fourier transform -- Fourier-type functional -- Gauss error function -- Wiener integrals; Primary 60J65 -- 28C20 -- 46E20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1918711
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In order to calculate the Wiener integrals for functionals on Wiener space, one can usually apply the change of variable theorem. But, there are many functionals that are difficult or impossible to calculate even when using the change of variable formula. In order to solve this problem, we establish an evaluation formula via the Fourier-type functionals on Wiener space. We then present various examples to which our evaluation formula can be applied and with the corresponding numerical approximations.