Characterizing abrupt transitions in stochastic dynamics
Data sampled at discrete times appears as a succession of discontinuous jumps, even if the underlying trajectory is continuous. We analytically derive a criterion that allows one to check whether for a given, even noisy time series the underlying process has a continuous (diffusion) trajectory or ha...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2018-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aaf0d7 |
| _version_ | 1797750588555919360 |
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| author | Klaus Lehnertz Lina Zabawa M Reza Rahimi Tabar |
| author_facet | Klaus Lehnertz Lina Zabawa M Reza Rahimi Tabar |
| author_sort | Klaus Lehnertz |
| collection | DOAJ |
| description | Data sampled at discrete times appears as a succession of discontinuous jumps, even if the underlying trajectory is continuous. We analytically derive a criterion that allows one to check whether for a given, even noisy time series the underlying process has a continuous (diffusion) trajectory or has jump discontinuities. This enables one to detect and characterize abrupt changes (jump events) in given time series. The proposed criterion is validated numerically using synthetic continuous and discontinuous time series. We demonstrate applicability of our criterion to distinguish diffusive and jumpy behavior by a data-driven inference of higher-order conditional moments from empirical observations. |
| first_indexed | 2024-03-12T16:35:58Z |
| format | Article |
| id | doaj.art-e8aac09c61de4040bd5d16eba0a30629 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:35:58Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-e8aac09c61de4040bd5d16eba0a306292023-08-08T14:55:37ZengIOP PublishingNew Journal of Physics1367-26302018-01-01201111304310.1088/1367-2630/aaf0d7Characterizing abrupt transitions in stochastic dynamicsKlaus Lehnertz0https://orcid.org/0000-0002-5529-8559Lina Zabawa1M Reza Rahimi Tabar2Department of Epileptology, University of Bonn , Sigmund-Freud-Straße 25, D-53105 Bonn, Germany; Helmholtz-Institute for Radiation and Nuclear Physics, University of Bonn , Nussallee 14–16, D-53115 Bonn, Germany; Interdisciplinary Center for Complex Systems, University of Bonn , Brühler Straße 7, D-53175 Bonn, GermanyDepartment of Epileptology, University of Bonn , Sigmund-Freud-Straße 25, D-53105 Bonn, Germany; Helmholtz-Institute for Radiation and Nuclear Physics, University of Bonn , Nussallee 14–16, D-53115 Bonn, GermanyDepartment of Physics, Sharif University of Technology , Tehran 11155-9161, Iran; Institute of Physics, Carl von Ossietzky University , D-26111 Oldenburg, GermanyData sampled at discrete times appears as a succession of discontinuous jumps, even if the underlying trajectory is continuous. We analytically derive a criterion that allows one to check whether for a given, even noisy time series the underlying process has a continuous (diffusion) trajectory or has jump discontinuities. This enables one to detect and characterize abrupt changes (jump events) in given time series. The proposed criterion is validated numerically using synthetic continuous and discontinuous time series. We demonstrate applicability of our criterion to distinguish diffusive and jumpy behavior by a data-driven inference of higher-order conditional moments from empirical observations.https://doi.org/10.1088/1367-2630/aaf0d7Kramers–Moyal coefficientsjump-diffusion processestemporal resolutionPawula theoremtime series analysis |
| spellingShingle | Klaus Lehnertz Lina Zabawa M Reza Rahimi Tabar Characterizing abrupt transitions in stochastic dynamics New Journal of Physics Kramers–Moyal coefficients jump-diffusion processes temporal resolution Pawula theorem time series analysis |
| title | Characterizing abrupt transitions in stochastic dynamics |
| title_full | Characterizing abrupt transitions in stochastic dynamics |
| title_fullStr | Characterizing abrupt transitions in stochastic dynamics |
| title_full_unstemmed | Characterizing abrupt transitions in stochastic dynamics |
| title_short | Characterizing abrupt transitions in stochastic dynamics |
| title_sort | characterizing abrupt transitions in stochastic dynamics |
| topic | Kramers–Moyal coefficients jump-diffusion processes temporal resolution Pawula theorem time series analysis |
| url | https://doi.org/10.1088/1367-2630/aaf0d7 |
| work_keys_str_mv | AT klauslehnertz characterizingabrupttransitionsinstochasticdynamics AT linazabawa characterizingabrupttransitionsinstochasticdynamics AT mrezarahimitabar characterizingabrupttransitionsinstochasticdynamics |