title: Fractional brownian motion versus the continuous-time random walk: a simple test for subdiffusive dynamics.
abstract: Fractional Brownian motion with Hurst index less then 1/2 and continuous-time random walk with heavy tailed waiting times (and the corresponding fractional Fokker-Planck equation) are two different processes that lead to a subdiffusive behavior widespread in complex systems. We propose a simple test, based on the analysis of the so-called p variations, which allows distinguishing between the two models on the basis of one realization of the unknown process. We apply the test to the data of Golding and Cox [Phys. Rev. Lett. 96, 098102 (2006)10.1103/PhysRevLett.96.098102], describing the motion of individual fluorescently labeled mRNA molecules inside live E. coli cells. It is found that the data does not follow heavy tailed continuous-time random walk. The test shows that it is likely that fractional Brownian motion is the underlying process.
authors.affiliation: Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland. marcin.magdziarz@pwr.wroc.pl
authors.forename: Marcin
authors.initials: M
authors.lastname: Magdziarz
authors.forename: Aleksander
authors.initials: A
authors.lastname: Weron
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Burnecki
authors.forename: Joseph
authors.initials: J
authors.lastname: Klafter