@misc{BurneckiWylomanskaChechkin2015,
  author    = {Burnecki, Krzysztof and Wylomanska, Agnieszka and Chechkin, Aleksei V.},
  title     = {Discriminating between light- and heavy-tailed distributions with limit theorem},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {495},
  issn      = {1866-8372},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-408172},
  pages     = {23},
  year      = {2015},
  abstract  = {In this paper we propose an algorithm to distinguish between light- and heavy-tailed probability laws underlying random datasets. The idea of the algorithm, which is visual and easy to implement, is to check whether the underlying law belongs to the domain of attraction of the Gaussian or non-Gaussian stable distribution by examining its rate of convergence. The method allows to discriminate between stable and various non-stable distributions. The test allows to differentiate between distributions, which appear the same according to standard Kolmogorov-Smirnov test. In particular, it helps to distinguish between stable and Student's t probability laws as well as between the stable and tempered stable, the cases which are considered in the literature as very cumbersome. Finally, we illustrate the procedure on plasma data to identify cases with so-called L-H transition.},
  language  = {en}
}
@misc{ŚlęzakBurneckiMetzler2019,
  author    = {Ślęzak, Jakub and Burnecki, Krzysztof and Metzler, Ralf},
  title     = {Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {765},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43792},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-437923},
  pages     = {18},
  year      = {2019},
  abstract  = {Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.},
  language  = {en}
}