Heavy-tailed fractional Pearson diffusions
Probability
2017-07-06 v1
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.
Cite
@article{arxiv.1707.01116,
title = {Heavy-tailed fractional Pearson diffusions},
author = {Nikolai N. Leonenko and Ivan Papić and Alla Sikorskii and Nenad Šuvak},
journal= {arXiv preprint arXiv:1707.01116},
year = {2017}
}