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Let denote the space of real-valued continuous functions on the interval with an analogue of Wiener measure and for a partition of , let and be given by and , respectively. In this paper, using a simple formula for the conditional -integral of functions on with the conditioning function , we derive a simple formula for the conditional -integral of the functions with the conditioning function . As applications of the formula with the function , we evaluate the conditional -integral...
Let denote a generalized Wiener space, the space of real-valued continuous functions on the interval , and define a random vector by
where , , and is a partition of . Using simple formulas for generalized conditional Wiener integrals, given we will evaluate the generalized analytic conditional Wiener and Feynman integrals of the functions in a Banach algebra which corresponds to Cameron-Storvick’s Banach algebra . Finally, we express the generalized analytic conditional Feynman...
In this paper, we introduce a simple formula for conditional Wiener integrals over , the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral...
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