Analytic continuation of the change of variable formula for smooth measures (Q951715)

From the text: We extend the Cameron-Martin-Girsanov-Maruyama-Ramer formulas to those transformations of smooth complex-valued measures on a locally convex space which are analytic continuations of transformations of smooth measures generated by (nonlinear) transformations of this space. We also show that, if the standard Feynman-Kac formula is assumed to be known, then the classical Feynman-Kac-Ito theorem turns out to be an immediate corollary of the generalized Girsanov-Maruyama formula. An important role in obtaining the results which we discuss is played by the notion of the logarithmic derivative of a function of a real argument taking values in the space of real (signed) measures.