Abstract
We study the chaos expansion transform, in short, chaos expansions, in a class of white noise spaces with series expansions by means of Hermite polynomials and functions, with certain weight sequences. Since Hermite polynomials are eigenfunctions for the Ornstein–Uhlenbeck operator, we apply the chaos expansion transform in solving of a class of equations. Moreover, we solve a generalized eigenvalue problem for the Malliavin derivative by means of chaos expansions.
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