Nonstationary Langevin equation: Statistical properties and application to explain effects observed in cardiological time series

Jens Kirchner, Wolfgang Meyer, Markus Elsholz, and Bernhard Hensel
Phys. Rev. E 76, 021110 – Published 16 August 2007

Abstract

Using the Langevin equation we develop the model of a stochastic process subject to a given time-dependent regulatory mechanism. The effects of this nonstationarity on the statistical properties of the time series, i.e., on global and conditional probability densities and on the moments of the distribution, are derived. Application of these results on simple model trends allows one to approximate cardiological data and thus to explain effects recently observed in the reconstruction of the deterministic part of the Langevin equation for time series of heart rate.

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  • Received 2 October 2006

DOI:https://doi.org/10.1103/PhysRevE.76.021110

©2007 American Physical Society

Authors & Affiliations

Jens Kirchner*, Wolfgang Meyer, Markus Elsholz, and Bernhard Hensel

  • Max Schaldach-Stiftungsprofessur, Center for Medical Physics and Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

  • *kirchner@biomed.uni-erlangen.de

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Issue

Vol. 76, Iss. 2 — August 2007

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