Change of scale formulas for conditional Wiener integrals as integral transforms over Wiener paths in abstract Wiener space
Commun. Korean Math. Soc. 2007 Vol. 22, No. 1, 91-109 Printed March 1, 2007
Dong Hyun Cho Kyonggi University
Abstract : In this paper, we derive a change of scale formula for conditional Wiener integrals, as integral transforms, of possibly unbounded functions over Wiener paths in abstract Wiener space. In fact, we derive the change of scale formula for the product of the functions in a Banach algebra which is equivalent to both the Fresnel class and the space of measures of bounded variation over a real separable Hilbert space, and the $L_p$-type cylinder functions over Wiener paths in abstract Wiener space. As an application of the result, we obtain a change of scale formula for the conditional analytic Fourier-Feynman transform of the product of the functions.
Keywords : change of scale formula, conditional analytic Feynman integral, conditional analytic Fourier-Feynman transform, conditional analytic Wiener integral, conditional Wiener integral