Gaussian diffusion interrupted by Lévy walk. (5th October 2016) - Weber, Piotr; Pepłowski, Piotr
Abstract: We investigate a stochastic process that links two processes in one model: Gaussian diffusion and one-sided Levy walks leading to anomalous diffusion. The motivation for our study is an observation of 'heavy-tailed' momentum probability density in a standard map and its modifications when accelerated modes emerge in the phase space. In this stochastic model, we derive a fractional differential equation for its probability density function. Numerical and analytical solutions for certain values of parameters are presented.