Abstract
Let denote a generalized Wiener space, the space of real-valued continuous functions on the interval , and define a random vector by where is a partition of and with almost everywhere. Using a simple formula for a generalized conditional Wiener integral on with the conditioning function , we evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function for , where , is a unit element in , and is the Fourier transform of a measure of bounded variation over . We then express the generalized analytic conditional Feynman integral of as two kinds of limits of nonconditional generalized Wiener integrals with a polygonal function and cylinder functions using a change-of-scale transformation. The choice of a complete orthonormal subset of used in the transformation is independent of .
Citation
Dong Hyun Cho. "Scale transformations for present position-dependent conditional expectations over continuous paths." Ann. Funct. Anal. 7 (2) 358 - 370, May 2016. https://doi.org/10.1215/20088752-3544830
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