@misc{VilkAghionAvgaretal.2022,
  author    = {Vilk, Ohad and Aghion, Erez and Avgar, Tal and Beta, Carsten and Nagel, Oliver and Sabri, Adal and Sarfati, Raphael and Schwartz, Daniel K. and Weiß, Matthias and Krapf, Diego and Nathan, Ran and Metzler, Ralf and Assaf, Michael},
  title     = {Unravelling the origins of anomalous diffusion},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1303},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-57764},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-577643},
  pages     = {16},
  year      = {2022},
  abstract  = {Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations ("Joseph effect"), fat-tailed probability density of increments ("Noah effect"), and nonstationarity ("Moses effect"). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.},
  language  = {en}
}
@misc{CherstvyVinodAghionetal.2017,
  author    = {Cherstvy, Andrey G. and Vinod, Deepak and Aghion, Erez and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Time averaging, ageing and delay analysis of financial time series},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-400541},
  pages     = {11},
  year      = {2017},
  abstract  = {We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.},
  language  = {en}
}