Title: Superstatistical generalized Langevin equation
Author: Jakub Ślęzak
We present a new superstatistical model based on the generalized Langevin equation and study its properties. Our aim is to propose a description of systems in which both complex (e.g. long range) memory is observed and the distribution is non-Gaussian. The studied model is relatively simple, it but shows a wide range of interesting and unusual properties, related to its non-Gaussian form of dependence and non-ergodicity. We explain in detail this behaviour and provide asymptotical formulas for tails of covariance and probability density in most typical cases. These results show an alternative to the standard superstatistical approach based on the random diffusion coefficient, which has a wide range of possible applications.