Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1151946 | Statistics & Probability Letters | 2014 | 10 Pages |
Abstract
The stochastic solution to diffusion equations with polynomial coefficients is called a Pearson diffusion. If the time derivative is replaced by a distributed order fractional derivative, the stochastic solution is called a distributed order fractional Pearson diffusion. This paper develops a formula for the covariance function of distributed order fractional Pearson diffusion in the steady state, in terms of generalized Mittag-Leffler functions. The correlation function decays like a power law. That formula shows that distributed order fractional Pearson diffusions exhibits long range dependence.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Jebessa B. Mijena, Erkan Nane,