CHANGE OF SCALE FORMULAS FOR CONDITIONAL WIENER INTEGRALS AS INTEGRAL TRANSFORMS OVER WIENER PATHS IN ABSTRACT WIENER SPACE

Title & Authors
CHANGE OF SCALE FORMULAS FOR CONDITIONAL WIENER INTEGRALS AS INTEGRAL TRANSFORMS OVER WIENER PATHS IN ABSTRACT WIENER SPACE
Cho, Dong-Hyun;

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 $\small{L_p-type}$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;
Language
English
Cited by
1.
GENERALIZED ANALYTIC FEYNMAN INTEGRAL VIA FUNCTION SPACE INTEGRAL OF BOUNDED CYLINDER FUNCTIONALS,;;;

대한수학회보, 2011. vol.48. 3, pp.475-489
1.
SCALE TRANSFORMATIONS FOR PRESENT POSITION-INDEPENDENT CONDITIONAL EXPECTATIONS, Journal of the Korean Mathematical Society, 2016, 53, 3, 709
2.
Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions, Journal of Function Spaces, 2016, 2016, 1
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