Anvari, Mehrnaz and Tabar, M. Reza Rahimi and Peinke, Joachim and Lehnertz, Klaus (2016) Disentangling the stochastic behavior of complex time series. Scientific Reports, 6 (1). ISSN 2045-2322

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Abstract

Complex systems involving a large number of degrees of freedom, generally exhibit non-stationary dynamics, which can result in either continuous or discontinuous sample paths of the corresponding time series. The latter sample paths may be caused by discontinuous events – or jumps – with some distributed amplitudes, and disentangling effects caused by such jumps from effects caused by normal diffusion processes is a main problem for a detailed understanding of stochastic dynamics of complex systems. Here we introduce a non-parametric method to address this general problem. By means of a stochastic dynamical jump-diffusion modelling, we separate deterministic drift terms from different stochastic behaviors, namely diffusive and jumpy ones, and show that all of the unknown functions and coefficients of this modelling can be derived directly from measured time series. We demonstrate applicability of our method to empirical observations by a data-driven inference of the deterministic drift term and of the diffusive and jumpy behavior in brain dynamics from ten epilepsy patients. Particularly these different stochastic behaviors provide extra information that can be regarded valuable for diagnostic purposes.

Item Type:	Article
Additional Information:	Publiziert mit Hilfe des DFG-geförderten Open Access-Publikationsfonds der Carl von Ossietzky Universität Oldenburg.
Uncontrolled Keywords:	Epilepsy, Statistical physics, thermodynamics and nonlinear dynamics
Subjects:	Science and mathematics > Physics
Divisions:	Faculty of Mathematics and Science > Institute of Physics (IfP)
Date Deposited:	20 Sep 2017 12:21
Last Modified:	20 Sep 2017 12:21
URI:	https://oops.uni-oldenburg.de/id/eprint/3282
URN:	urn:nbn:de:gbv:715-oops-33630
DOI:	doi:10.1038/srep35435
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