Year: 2021
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Zhang, Benjamin J., Sahai, Tuhin, Marzouk, Youssef M.
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3205151056