Evaluation Formula and Approximation for Wiener Integrals via the Fourier-Type Functional

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.

Keywords:

• Evaluation formula
• Fourier transform
• Fourier-type functional
• Gauss error function
• Wiener integrals

2000 MATHEMATICS SUBJECT CLASSIFICATION.:

• Primary 60J65
• 28C20
• 46E20

Acknowledgments

The authors thank the referees for their helpful suggestions which led to the present version of this paper.