Random Walks Models with Intermediate Fractional Diffusion Asymptotics

摘要

Random walk process was investigated with PDF of random time intervals similar to fractional exponential law on small times and to regular exponential law on long times. Generalized fractional Kolmogorov-Feller equation was derived for such kind of process. Asymptotics of it's PDF in the long time limit and for intermediate times were found. They obey standart diffusion law or fractional diffusion law resprectively. Exact solutions of mentioned equations were numerically calculated, demonstrating crossover of fractional diffusion law into the linear one.