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The effect of drift on the Fourier-Feynman transform, the convolution product and the first variation. (English) Zbl 0976.28008

In this paper, the authors examine the effects that drift has on the various relationships that occur among the Fourier-Feynman transform, the convolution product, and the first variation for various functionals on the Wiener space. In fact, they examine the effect of drift on “transforms and variations” and on “convolutions and variations” and show how drift effects the relationships involving all three of the concepts of transforms, convolutions and variations where each concept is used precisely once. They also obtain several interesting formulas for these various relationships.

MSC:

28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
60J65 Brownian motion