TY  - GEN
A1  - Ślęzak, Jakub
A1  - Burnecki, Krzysztof
A1  - Metzler, Ralf
T1  - Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
T2  - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2  - 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, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 765 
KW  - diffusion
KW  - Langevin equation
KW  - Brownian yet non-Gaussian diffusion
KW  - diffusing diffusivity
KW  - superstatistics
KW  - autoregressive models
KW  - time series analysis
KW  - codifference
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-437923
SN  - 1866-8372
IS  - 765
ER  - 
TY  - JOUR
A1  - Ślęzak, Jakub
A1  - Burnecki, Krzysztof
A1  - Metzler, Ralf
T1  - Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
JF  - New Journal of Physics
N2  - 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, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.
KW  - diffusion
KW  - Langevin equation
KW  - Brownian yet non-Gaussian diffusion
KW  - diffusing diffusivity
KW  - superstatistics
KW  - autoregressive models
KW  - time series analysis
KW  - codifference
Y1  - 2019
U6  - https://doi.org/10.1088/1367-2630/ab3366
SN  - 1367-2630
VL  - 21
PB  - Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
CY  - Bad Honnef und London
ER  - 
TY  - GEN
A1  - Ślęzak, Jakub
A1  - Metzler, Ralf
A1  - Magdziarz, Marcin
T1  - Codifference can detect ergodicity breaking and non-Gaussianity
T2  - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2  - 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 dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 748 
KW  - diffusion
KW  - anomalous diffusion
KW  - stochastic time series
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436178
IS  - 748
ER  - 
TY  - JOUR
A1  - Ślęzak, Jakub
A1  - Metzler, Ralf
A1  - Magdziarz, Marcin
T1  - Codifference can detect ergodicity breaking and non-Gaussianity
JF  - New Journal of Physics
N2  - 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 dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.
KW  - diffusion
KW  - stochastic time series
KW  - anomalous diffusion
Y1  - 2019
U6  - https://doi.org/10.1088/1367-2630/ab13f3
SN  - 1367-2630
VL  - 21
PB  - Deutsche Physikalische Gesellschaft
CY  - Bad Honnef
ER  -