They includes Ornstein-Uhlenbeck, Cox-Ingersoll-Ross, and several others
wellkown processes. Their stationary distributions solve the Pearson equation,
developed by Pearson in 1914 to unify some important classes of distributions
(e.g., normal, gamma, beta). Their eigenfunction expansions involve the traditional
classes of orthogonal polynomials (e.g., Hermite, Laguerre, Jacobi). We develop
fractional Pearson di¢ sions ([1],[2]), constructing by a non-Markovian inverse
stable time change. Their transition densities are shown to solve a time-fractional
analogue to the diffusion equation with polynomial coefficients. Because this process
is not Markovian, the stochastic solution provides additional information about
the movement of particles that di§use under this model. This is joint work
with M.M. Meerschaert and A. Sikorskii (Michigan State Univeraity, USA).
Anomalous diffusions have proven useful in applications to physics,
geophysics, chemistry, and finance.


Marco Ferrante