Correlation Structure of Time-Changed Pearson Diffusions

• Activity Number: 228
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Jebessa Mijena*+
• Companies: Georgia College & State University
• Keywords: Pearson diffusion ; Fractional derivative ; Correlation function ; Generalized Mittag-Leffler function

Abstract

The stochastic solution to diffusion equations with polynomial coefficients is called a Pearson diffusion. If the time derivative is replaced by a distributed fractional derivative, the stochastic solution is called a fractional Pearson diffusion. This paper develops a formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of generalized 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 smallest order of the distributed fractional derivative.