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White Noise Analysis and Chaos Expansions

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Equations Involving Malliavin Calculus Operators

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Abstract

In the framework of white noise analysis, random variables and stochastic processes can be represented in terms of Fourier series in a Hilbert space orthogonal basis, namely in their chaos expansion forms. We briefly summarize basic concepts and notations of white noise analysis, characterize different classes of stochastic processes (test, square integrable and generalized stochastic processes) in terms of their chaos expansion representations and review the main properties of the Wick calculus and stochastic integration.

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Authors and Affiliations

  1. Department of Mathematics, University of Innsbruck, Innsbruck, Austria

    Tijana Levajković

  2. Department of Mathematics, Yachay Tech, San Miguel de Urcuquí, Ecuador

    Hermann Mena

  3. Department of Mathematics, University of Innsbruck, Innsbruck, Austria

    Hermann Mena

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  1. Tijana Levajković
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  2. Hermann Mena
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Correspondence to Tijana Levajković .

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Levajković, T., Mena, H. (2017). White Noise Analysis and Chaos Expansions. In: Equations Involving Malliavin Calculus Operators. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-65678-6_1

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