Relationships among transforms, convolutions, and first variations (Q1283422)
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scientific article; zbMATH DE number 1275572
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Relationships among transforms, convolutions, and first variations |
scientific article; zbMATH DE number 1275572 |
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Relationships among transforms, convolutions, and first variations (English)
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18 February 2004
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Summary: In this paper, we establish several interesting relationships involving the Fourier-Feynman transform, the convolution product, and the first variation for functionals \(F\) on the Wiener space of the form \(F(x)= f(\langle\alpha_1,x\rangle,\dots,\langle\alpha_n,x\rangle)\), where \(\langle\alpha_j,x\rangle\) denotes the Paley-Wiener-Zygmund stochastic integral \(\int^T_0\alpha_j(t) dx(t)\).
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Fourier-Feynman transform
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convolution product
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first variation for functionals
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Wiener space
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Paley-Wiener-Zygmund stochastic integral
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