Long-Memory and Features of Fluctuation in A Fractional Generalized Cauchy Process

Abstract

A fractional generalized Cauchy process (FGCP) is studied, which may give the same probability density function as the ordinary generalized Cauchy process. The exact solution of the Fokker-Planck equation for FGCP is given with the aid of the inverse Lévy transform. The associated eigenvalue problem is clarified. It is also exhibited the natures of long-memory, fractal, and volatility clustering associated with the FGCP.