Wick Analysis for Bernoulli Noise Functionals

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2014 English Publisher:WileyJournal:Journal of Function Spaces, volume 2,014, pages 1-7 (issn: 2314-8896, eissn: 2314-8888,

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Authors: Caishi Wang; Jihong Zhang;

doi: 10.1155/2014/727341

Wick Analysis for Bernoulli Noise Functionals

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Abstract

A Gel’fand tripleS(Ω)⊂L2(Ω)⊂S*(Ω)is constructed of functionals ofZ, whereZ=(Zn)n∈ℕis an appropriate Bernoulli noise on a probability space(Ω,ℱ,ℙ). Characterizations are given to bothS(Ω)andS*(Ω). It is also shown that a Wick-type product can be defined onS*(Ω)and moreoverS*(Ω)forms a commutative algebra with the product. Finally, a transform namedS-transform is defined onS*(Ω)and its continuity as well as other properties are examined.

Related Organizations

Northeast Normal University
China (People's Republic of)
Northwest Normal University
China (People's Republic of)

Keywords

Bernoulli noise, QA1-939, Integral transforms in distribution spaces, Gel'fand triple, White noise theory, Wick-type product, Mathematics

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