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...

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Bibliographic Details
Published inNew journal of physics Vol. 20; no. 11; pp. 113043 - 113055
Main Authors Lehnertz, Klaus, Zabawa, Lina, Tabar, M Reza Rahimi
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 30.11.2018
Subjects
Change detection
Criteria
Empirical analysis
jump-diffusion processes
Kramers-Moyal coefficients
Pawula theorem
Physics
temporal resolution
Time series
time series analysis
Trajectory analysis
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Summary: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.
Bibliography:NJP-108763.R2
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/aaf0d7