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

Young Sik Kim

 Global Analysis Research Center, Seoul National University, Seoul 151-742, Korea
Received 24 April 1996; Revised 12 August 1996

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.