Abstract
Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.
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This work was supported by the National Natural Science Foundation of China. This paper is an enlargement and revised version of the paper entitled “Products and Transforms of White-Noise Functionals” (preprint, 1990).
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Yan, J.A. Products and transforms of white-noise functionals (in general setting). Appl Math Optim 31, 137–153 (1995). https://doi.org/10.1007/BF01182785
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DOI: https://doi.org/10.1007/BF01182785
Key words
- White-noise analysis
- Wiener and Wick products
- Wick tensor power
- Scaling transformation
- Translation
- Sobolev derivative
- Gradient operator