期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 66, 期 5, 页码 737-745出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2013.01.009
关键词
Pearson diffusion; Fractional derivative; Correlation function; Mittag-Leffler function
资金
- European Commission [PIRSES-GA-2008-230804]
- NSF [DMS-1025486]
- NIH [R01-EB012079]
- Division Of Earth Sciences
- Directorate For Geosciences [1344280] Funding Source: National Science Foundation
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. (C) 2013 Elsevier Ltd. All rights reserved.
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