International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 73-78
doi:10.1155/S0161171298000088

A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space

Abstract

The purpose of this paper is to establish the existence of analytic Wiener and Feynman integrals for a class of certain cylinder functions which is of the form: F(x)=f((h1,x)∼,⋯,(hn,x)∼),    x∈B, on the abstract Wiener space, and to establish the relationship between the Wiener integral and the analytic Feynman integral for such cylinder functions on the abstract Wiener space. We then establish a change of scale formula for Wiener integrals of such cylinder functions on the abstract Wiener space.