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Symmetric Diffusions with Polynomial Eigenvectors

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Stochastic Analysis and Applications 2014

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 100))

Abstract

We describe symmetric diffusion operators where the spectral decomposition is given through a family of orthogonal polynomials. In dimension one, this reduces to the case of Hermite, Laguerre and Jacobi polynomials. In higher dimension, some basic examples arise from compact Lie groups. We give a complete description of the bounded sets on which such operators may live. We then provide in dimension \(2\) a classification of those sets when the polynomials are ordered according to their usual degrees.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 Route de Narbonne, 31062, Toulouse, France

    Dominique Bakry

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  1. Dominique Bakry
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Correspondence to Dominique Bakry .

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Editors and Affiliations

  1. Department of Mathematics, Imperial College, London, United Kingdom

    Dan Crisan

  2. Mathematical Institute, University of Oxford, Oxford, United Kingdom

    Ben Hambly

  3. Department of Mathematics and IROM, University of Texas McCombs School of Business, Austin, Texas, USA

    Thaleia Zariphopoulou

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Bakry, D. (2014). Symmetric Diffusions with Polynomial Eigenvectors. In: Crisan, D., Hambly, B., Zariphopoulou, T. (eds) Stochastic Analysis and Applications 2014. Springer Proceedings in Mathematics & Statistics, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-319-11292-3_2

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