Wick Analysis for Bernoulli Noise Functionals

Abstract EN

A Gel’fand triple S ( Ω ) ⊂ L 2 ( Ω ) ⊂ S * ( Ω ) is constructed of functionals of Z , where Z = ( Z n ) n ∈ ℕ is an appropriate Bernoulli noise on a probability space ( Ω , ℱ , ℙ ) .

Characterizations are given to both S ( Ω ) and S * ( Ω ) .

It is also shown that a Wick-type product can be defined on S * ( Ω ) and moreover S * ( Ω ) forms a commutative algebra with the product.

Finally, a transform named S -transform is defined on S * ( Ω ) and its continuity as well as other properties are examined.