Stochastic systems driven by Levy noises: Relaxation and equilibrium

We present a short review on the Langevin and the kinetic description of stochastic systems driven by Levy noises obeying Levy stable probability laws. The class of Levy stable noises is the natural generalization of a widely used Gaussian noise, since the Levy stable distributions obey the Generalized Central Limit Theorem. It implies that just these laws (as the Gaussian one) occur when the evolution of a stochastic system or the result of an experiment are determined by the sum of a large number of random factors. The kinetic description of the Levy driven stochastic systems requires the use of the kinetic equations with partial derivatives of fractional orders. The topics considered are as follows: derivation of fractional Eitistein-Smoluchowsky kinetic equation; relaxation in external fields; non-Boltzmann equilibrium.