Leonenko, Nikolai N. ![]() |
Official URL: http://dx.doi.org/10.1016/j.camwa.2013.01.009
Abstract
The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long-range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.
Item Type: | Article |
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Date Type: | Publication |
Status: | Published |
Schools: | Mathematics |
Subjects: | Q Science > QA Mathematics |
Uncontrolled Keywords: | Pearson diffusion; Fractional derivative; Correlation function; Mittag-Leffler function |
Publisher: | Elsevier |
ISSN: | 0898-1221 |
Last Modified: | 24 Oct 2022 10:38 |
URI: | https://orca.cardiff.ac.uk/id/eprint/45214 |
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