title: Disentangling the stochastic behavior of complex time series.
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 appli- cability 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.
authors.affiliation: Institute of Physics and ForWind, Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany.
authors.forename: Mehrnaz
authors.initials: M
authors.lastname: Anvari
authors.affiliation: Institute of Physics and ForWind, Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany.|Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran.
authors.forename: M Reza Rahimi
authors.initials: MR
authors.lastname: Tabar
authors.affiliation: Institute of Physics and ForWind, Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany.
authors.forename: Joachim
authors.initials: J
authors.lastname: Peinke
authors.affiliation: Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany.|Helmholtz-Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany.|Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany.
authors.forename: Klaus
authors.initials: K
authors.lastname: Lehnertz
mesh_terms: D000465:Algorithms; D001519:Behavior; D001921:Brain / Q000502:physiology; D006801:Humans; D008962:Models, Theoretical; D013269:Stochastic Processes