Fractional brownian motion versus the continuous-time random walk: A simple test for subdiffusive dynamics

Marcin Magdziarz, Aleksander Weron, Krzysztof Burnecki, Joseph Klafter

Research output: Contribution to journalArticlepeer-review

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, 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.

Original languageEnglish
Article number180602
JournalPhysical Review Letters
Volume103
Issue number18
DOIs
StatePublished - 30 Oct 2009

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