Heavy-tailed fractional Pearson diffusions

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, 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:	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:	18 Nov 2024 15:45
URI:	https://orca.cardiff.ac.uk/id/eprint/98905

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