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Relationships between generalized Wiener integrals and conditional analytic Feynman integrals over continuous paths

Byoung Soo KimDong Hyun Cho — 2017

Czechoslovak Mathematical Journal

Let C [ 0 , t ] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [ 0 , t ] , and define a random vector Z n : C [ 0 , t ] n + 1 by Z n ( x ) = x ( 0 ) + a ( 0 ) , 0 t 1 h ( s ) d x ( s ) + x ( 0 ) + a ( t 1 ) , , 0 t n h ( s ) d x ( s ) + x ( 0 ) + a ( t n ) , where a C [ 0 , t ] , h L 2 [ 0 , t ] , and 0 < t 1 < < t n t is a partition of [ 0 , t ] . Using simple formulas for generalized conditional Wiener integrals, given Z n we will evaluate the generalized analytic conditional Wiener and Feynman integrals of the functions F in a Banach algebra which corresponds to Cameron-Storvick’s Banach algebra 𝒮 . Finally, we express the generalized analytic conditional Feynman...

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