Correlation structure of fractional Pearson diffusions

Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091, Meerschaert, Mark M. and Sikorskii, Alla 2013. Correlation structure of fractional Pearson diffusions. Computers & Mathematics with Applications 66 (5) , pp. 737-745. 10.1016/j.camwa.2013.01.009

Full text not available from this repository.

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
Date Type:	Publication
Status:	Published
Schools:	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

Citation Data

Cited 44 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item