Time Scale Transformation in Bivariate Pearson Diffusions: A Shift from Light to Heavy Tails

Abstract

Heavy-tailed Pearson diffusions provide a natural alternative to well-known Ornstein–Uhlenbeck and Cox–Ingersoll–Ross processes in applications that require addressing heavy-tailed behavior. In this paper, all three heavy-tailed Pearson diffusions, having inverse gamma, Fisher–Snedecor and Student stationary distributions, are constructed via an absolutely continuous time-change process employed in a specific functional transformation of CIR or OU. Moreover, time-change rates in stochastic clocks are continuous functionals of the CIR process.

Keywords

• Pearson distribution
• heavy-tailed Pearson diffusion
• Cox–Ingersoll–Ross process
• Ornstein–Uhlenbeck process
• time-change process