69 citations · 149 across the 7 of their papers we have counts for
8 papers
Improved mean squared displacement analysis for anomalous single particle trajectories
Jakub Ślęzak, Joanna Janczura, Diego Krapf +1
The mean squared displacement (MSD) is a cornerstone in the analysis of diffusion processes in complex media. When the system is heterogeneous and, in particular, when single-parti…
Minimal model of diffusion with time changing Hurst exponent
Jakub Slezak, Ralf Metzler
We introduce the stochastic process of incremental multifractional Brownian motion (IMFBM), which locally behaves like fractional Brownian motion with a given local Hurst exponent…
Memory-multi-fractional Brownian motion with continuous correlations
Wei Wang, Michal Balcerek, Krzysztof Burnecki +6
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-depe…
From diffusion in compartmentalized media to non-Gaussian random walks
Jakub Ślęzak, Stanislav Burov
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartme…
Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
Jakub Ślęzak, Krzysztof Burnecki, Ralf Metzler
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,…
Codifference can detect ergodicity breaking and non-Gaussianity
Jakub Slezak, Ralf Metzler, Marcin Magdziarz
We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of…
Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
Jakub Ślęzak, Ralf Metzler, Marcin Magdziarz
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian…
From physical linear systems to discrete-time series. A guide for analysis of the sampled experimental data
Jakub Ślęzak, Aleksander Weron
Modelling physical data with linear discrete time series, namely Fractionally Integrated Autoregressive Moving Average (ARFIMA), is a technique which achieved attention in recent y…