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 ∈ 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...

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Bibliographic Details
Published in:Journal of function spaces 2014-01, Vol.2014 (2014), p.1-7
Main Authors: Wang, Caishi, Zhang, Jihong
Format: Article
Language:English
Subjects:
Algebra
Construction
Continuity
Function space
Functionals
Mathematical functions
Noise
Partial differential equations
Probability
Quantum field theory
Random variables
Stochastic models
Transforms
Wicks
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Summary: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.
ISSN:2314-8896
2314-8888
DOI:10.1155/2014/727341