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arXiv · 1707.01116

Heavy-tailed fractional Pearson diffusions

Nikolai N. Leonenko·Ivan Papić·Alla Sikorskii·Nenad Šuvak
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Abstract

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian 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.

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Nikolai N. Leonenko, Ivan Papić, Alla Sikorskii, Nenad Šuvak. 2017-07-04. Heavy-tailed fractional Pearson diffusions. https://doi.org/10.1016/j.spa.2017.03.004

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