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Article Dans Une Revue Results in mathematics = Resultate der Mathematik Année : 2021

On three families of Karhunen-Loève expansions associated with classical orthogonal polynomials

Résumé

We introduce three families of positive definite bivariate integral kernels whose eigenfunctions and eigenvalues can be explicitly derived in terms of classical orthogonal polynomials. All sequences of classical orthogonal polynomials are involved in at least one of our developments. We show that the well-known Karhunen–Loève expansions of the Wiener, Brownian bridge and Anderson–Darling Gaussian stochastic processes are particular cases of our results.
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Dates et versions

hal-03243167 , version 1 (31-05-2021)

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Jean-Renaud Pycke. On three families of Karhunen-Loève expansions associated with classical orthogonal polynomials. Results in mathematics = Resultate der Mathematik, 2021, 76 (3), pp.148. ⟨10.1007/s00025-021-01454-x⟩. ⟨hal-03243167⟩
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