Computing eigenfunctions of the multidimensional Ornstein-Uhlenbeck operator

Benjamin J. Zhang; Tuhin Sahai; Youssef M. Marzouk

Computing eigenfunctions of the multidimensional Ornstein-Uhlenbeck operator

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arxiv 2110.09229 v1 pith:5O4EQJZO submitted 2021-10-07 math.NA cs.NAmath.PR

Benjamin J. Zhang , Tuhin Sahai , Youssef M. Marzouk This is my paper · ORCID

classification math.NAcs.NAmath.PR

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We discuss approaches to computing eigenfunctions of the Ornstein--Uhlenbeck (OU) operator in more than two dimensions. While the spectrum of the OU operator and theoretical properties of its eigenfunctions have been well characterized in previous research, the practical computation of general eigenfunctions has not been resolved. We review special cases for which the eigenfunctions can be expressed exactly in terms of commonly used orthogonal polynomials. Then we present a tractable approach for computing the eigenfunctions in general cases and comment on its dimension dependence.

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