SOLVING THE GENERALIZED LANGEVIN EQUATION WITH THE ALGEBRAICALLY CORRELATED NOISE

We solve the Langevin equation with the memory kernel. The stochastic force possesses algebraic correlations, proportional to 1/t. The veloc ity autocorrelation function and related quantities characterizing tra nsport properties are calculated with the assumption that the system i s in thermal equilibrium. Stochastic trajectories are simulated numeri cally, using the kangaroo process as a noise generator. Results of thi s simulation resemble Levy walks with divergent moments of the velocit y distribution. We consider motion of a Brownian particle, both withou t any external potential and in the harmonic oscillator held, in parti cular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle.