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Correlation structure of time-changed Pearson diffusions

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  • Mijena, Jebessa B.
  • Nane, Erkan

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.

Suggested Citation

  • Mijena, Jebessa B. & Nane, Erkan, 2014. "Correlation structure of time-changed Pearson diffusions," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 68-77.
    • Handle: RePEc:eee:stapro:v:90:y:2014:i:c:p:68-77
    DOI: 10.1016/j.spl.2014.03.020
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    Cited by:

    1. Almeida, Ricardo & Morgado, M. Luísa, 2018. "The Euler–Lagrange and Legendre equations for functionals involving distributed–order fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 394-403.

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