Conditional function space integrals with applications. (English) Zbl 0864.28006

Authors’ abstract: “In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we first consider a conditional function space integral for functionals of more general stochastic process and obtain an evaluation formula of the conditional function space integral. We then use this formula to derive the generalized Kac-Feynman integral equation and also to obtain a Cameron-Martin type translation theorem for our conditional function space integrals. These results subsume similar known results obtained by Chung and Kang, Park and Skoug and Yeh for the standard Wiener process”.


28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
60B11 Probability theory on linear topological spaces
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