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Article Dans Une Revue Stochastics: An International Journal of Probability and Stochastic Processes Année : 2013

Spectral representation of transition density of Fisher-Snedecor diffusion

N.N. Leonenko
  • Fonction : Auteur
N. Šuvak
  • Fonction : Auteur

Résumé

We analyse spectral properties of an ergodic heavy-tailed diffusion with the Fisher-Snedecor invariant distribution and compute spectral representation of its transition density. The spectral representation is given in terms of a sum involving finitely many eigenvalues and eigenfunctions (Fisher-Snedecor orthogonal polynomials) and an integral over the absolutely continuous spectrum of the corresponding Sturm-Liouville operator. This result enables the computation of the two-dimensional density of the Fisher-Snedecor diffusion as well as calculation of moments of the form, where m and n are at most equal to the number of Fisher-Snedecor polynomials. This result is particularly important for explicit calculations associated with this process. © 2013 Copyright Taylor and Francis Group, LLC.
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Dates et versions

hal-00867030 , version 1 (27-09-2013)

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Citer

Florin Avram, N.N. Leonenko, N. Šuvak. Spectral representation of transition density of Fisher-Snedecor diffusion. Stochastics: An International Journal of Probability and Stochastic Processes, 2013, 85 (2), pp.346-369. ⟨10.1080/17442508.2013.775285⟩. ⟨hal-00867030⟩
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