Analytic Feynman Integral and a Change of Scale Formula for Wiener Integrals of an Unbounded Cylinder Function. (17th October 2020) - Young Sik, Kim
Abstract : We investigate the behavior of the unbounded cylinder function F x = ∫ 0 T α 1 t d x t 2 k ⋅ ∫ 0 T α 2 t d x t 2 k ⋅ ⋯ ⋅ ∫ 0 T α n t d x t 2 k, 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 .