A recurrence formula with respect to the Cameron–Storvick type theorem of the 𝒯-transform

ABSTRACT

In this paper, we define a transform which has the kernel in its definition and a concept of derivative for functionals on Wiener space. We then establish some results and formulas for the transforms of functionals on Wiener space. We also establish the Cameron–Storvick type theorem for the transform. Finally, we obtain the recurrence formula for the transforms to evaluate formulas involving the multi-dimensional derivative.

KEYWORDS:

• Integral transform with the kernel
• Cameron–Storvick type theorem
• multi-dimensional derivative
• recurrence formula

AMS SUBJECT CLASSIFICATIONS:

• 44A20
• 44A15
• 33E99
• 28C20

Acknowledgments

The authors would like to express their gratitude to the referees for their valuable comments and suggestions which have improved the original paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hyun Soo Chung http://orcid.org/0000-0003-1458-7087