Annuncio di seminario:
Mercoledì 2 Luglio alle ore 12.00 in Aula 2BC30 del Dipartimento di Matematica dell'Università di Padova il Prof. Nikolai Leonenko dell'Università di Cardiff terrà il seminario
Titolo: Fractional Pearson diffusions.
Abstract: Pearson diffusions have stationary distributions of Pearson type. 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