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
Global Analysis Research Center, Seoul National University, Seoul 151-742, Korea
Received 24 April 1996; Revised 12 August 1996
Copyright © 1998 Young Sik Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.