Bystryk Y. Anomalous transport and relaxation processes in stochastic systems with ultraslow evolution

The thesis is devoted to the investigation of the anomalous transport behavior of stochastic systems which are characterized by Levy statistics and ultraslow evolution, and to the studying of the phenomenon of anomalous relaxation in two-state systems, properties of elements of which evolve according to the dichotomous process. Limiting probability densities and corresponding scaling functions which describe the asymptotic in time behavior of ultraslow Levy flights were determined. Anomalous transport properties of such processes were studied. The integral equation which describes relaxation in two-state systems was derived. It was obtained a number of anomalous asymptotic and exact solutions of this equation.