Wick Analysis for Bernoulli Noise Functionals. (12th March 2014)

• Record Type: Journal Article
• Authors: Wang, Caishi; Zhang, Jihong
• Other Names: Yang Dachun Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-03-12
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/727341
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : A Gel'fand tripleS ( Ω ) ⊂ L 2 ( Ω ) ⊂ S * ( Ω ) is constructed of functionals ofZ, whereZ = ( Z n ) n ∈ ℕ is 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.