Single-trajectory spectral analysis of scaled Brownian motion

A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, $T\to \infty $. In many experimental...

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Detalles Bibliográficos
Autores: Sposini, V., Metzler, R., Oshanin, G.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1010
Acceso en línea:http://hdl.handle.net/20.500.11824/1010
Access Level:acceso abierto
Palabra clave:diffusion
anomalous diffusion
power spectral analysis
single trajectory analysis
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spelling Single-trajectory spectral analysis of scaled Brownian motionSposini, V.Metzler, R.Oshanin, G.diffusionanomalous diffusionpower spectral analysissingle trajectory analysisA standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, $T\to \infty $. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit $T\to \infty $ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion. We demonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent. We also compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing single-trajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.Open Access Publication Fund of Potsdam University.201920192019info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1010reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://iopscience.iop.org/article/10.1088/1367-2630/ab2f52info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/10102026-06-19T12:47:47Z
dc.title.none.fl_str_mv Single-trajectory spectral analysis of scaled Brownian motion
title Single-trajectory spectral analysis of scaled Brownian motion
spellingShingle Single-trajectory spectral analysis of scaled Brownian motion
Sposini, V.
diffusion
anomalous diffusion
power spectral analysis
single trajectory analysis
title_short Single-trajectory spectral analysis of scaled Brownian motion
title_full Single-trajectory spectral analysis of scaled Brownian motion
title_fullStr Single-trajectory spectral analysis of scaled Brownian motion
title_full_unstemmed Single-trajectory spectral analysis of scaled Brownian motion
title_sort Single-trajectory spectral analysis of scaled Brownian motion
dc.creator.none.fl_str_mv Sposini, V.
Metzler, R.
Oshanin, G.
author Sposini, V.
author_facet Sposini, V.
Metzler, R.
Oshanin, G.
author_role author
author2 Metzler, R.
Oshanin, G.
author2_role author
author
dc.subject.none.fl_str_mv diffusion
anomalous diffusion
power spectral analysis
single trajectory analysis
topic diffusion
anomalous diffusion
power spectral analysis
single trajectory analysis
description A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, $T\to \infty $. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit $T\to \infty $ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion. We demonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent. We also compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing single-trajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019
2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1010
url http://hdl.handle.net/20.500.11824/1010
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://iopscience.iop.org/article/10.1088/1367-2630/ab2f52
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
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