Wick Analysis for Bernoulli Noise Functionals. (12th March 2014) - Wang, Caishi; Zhang, Jihong
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.