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Correlation structure of time-changed Pearson diffusions |
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| Affiliation: | 1. 231 W. Hancock St, Campus Box 17, Department of Mathematics, Georgia College & State University, Milledgeville, GA 31061, United States;2. 221 Parker Hall, Department of Mathematics and Statistics, Auburn University, Auburn, Al 36849, United States;1. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Complesso di Monte S. Angelo via Cintia, 80126 Napoli, Italy;2. Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, via Pietro Castellino 111, 80131 Napoli, Italy |
| 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. |
| Keywords: | Pearson diffusion Fractional derivative Correlation function Generalized Mittag-Leffler function |
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