Analytic Feynman integral and a change of scale formula for Wiener integrals of an unbounded cylinder function

Abstract

We investigate the behavior of the unbounded cylinder function F(x) = (integral(T)(0) alpha(1)(t)dx(t))(2k) . (integral(T)(0) alpha(2)(t)dx(t))(2k) ... (integral(T)(0) alpha(n) (t)dx(t))(2k), k = 1, 2, ... whose analytic Wiener integral and analytic Feynman integral exist, we prove some relationships among the analytic Wiener integral, the analytic Feynman integral, and the Wiener integral, and we prove a change of scale formula for the Wiener integral about the unbounded function on the Wiener space C-0[0, T].