43 citations · 43 across the 1 of their papers we have counts for
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Large deviations of time-averaged statistics for Gaussian processes
J. Gajda, A. Wylomanska, H. Kantz +2
In this paper we study the large deviations of time averaged mean square displacement (TAMSD) for Gaussian processes. The theory of large deviations is related to the exponential d…
Probabilistic properties of detrended fluctuation analysis for Gaussian processes
G. Sikora, M. Hoell, A. Wylomanska +3
The detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range correlations in time series. Although DFA has found many interesting a…
Optimal parameters for anomalous diffusion exponent estimation from noisy data
Yann Lanoiselée, Denis S. Grebenkov, Grzegorz Sikora +2
The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square…
Statistical test for fractional Brownian motion based on detrending moving average algorithm
Grzegorz Sikora
Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular…