Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
472497 | Computers & Mathematics with Applications | 2013 | 9 Pages |
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Nikolai N. Leonenko, Mark M. Meerschaert, Alla Sikorskii,