The behavior of conditional Wiener integrals on product Wiener space (Q2852448)

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scientific article; zbMATH DE number 6214127
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The behavior of conditional Wiener integrals on product Wiener space
scientific article; zbMATH DE number 6214127

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    The behavior of conditional Wiener integrals on product Wiener space (English)
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    8 October 2013
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    conditional Wiener integral
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    multiple conditional analytic Feynman integral
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    multiple conditional analytic Fourier-Feynman transform
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    multiple conditional analytic convolution product
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    first variation
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    \(n\)-dimensional Wiener directional derivative
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    The authors summarize the content of this paper in the following abstract: We first investigate the behavior of conditional Wiener integrals on product Wiener spaces and then proceed to establish a Fubini theorem for conditional Wiener integrals. We then define a very general multiple conditional analytic Fourier-Feynman transform and a multiple conditional analytic convolution product for functionals on Wiener spaces and then establish a relationship between them. Next, we obtain a basic formula for the conditional Wiener integral involving the first variation and the \(n\)-dimensional Wiener directional derivative. Finally, we establish several evaluation formulas for conditional Wiener and Feynman integrals involving the \(n\)-dimensional Wiener directional derivative of functionals on Wiener spaces.
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