Wick analysis for bernoulli noise functionals

A gel'fand triple s (ω) ⊂ l 2 (ω) ⊂ s (ω) is constructed of functionals of z,where z = (z n) n is an appropriate bernoulli noise on a probability space (ω,&fouriertrf). 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. © 2014 caishi wang and jihong zhang.