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Heavy-tailed fractional Pearson diffusions

Leonenko, Nikolai, Papic, I., Sikorskii, A. and Suvak, N. 2017. Heavy-tailed fractional Pearson diffusions. Stochastic Processes and their Applications 127 (11) , pp. 3512-3535. 10.1016/j.spa.2017.03.004

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Abstract

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a nonMarkovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Elsevier
ISSN: 0304-4149
Date of First Compliant Deposit: 13 March 2017
Date of Acceptance: 7 March 2017
Last Modified: 26 Apr 2018 18:00
URI: http://orca.cf.ac.uk/id/eprint/98905

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