Wick Analysis for Bernoulli Noise Functionals

Caishi Wang, Jihong Zhang
2014 Journal of Function Spaces  
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.
doi:10.1155/2014/727341 fatcat:re4v255qpbaq7i3nx27wf7zwty