Kernel-based regression of drift and diffusion coefficients of stochastic processes |
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Authors: | David Lamouroux Klaus Lehnertz |
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Affiliation: | aDepartment of Epileptology, University of Bonn, Germany;bHelmholtz-Institute for Radiation and Nuclear Physics, University of Bonn, Germany;cInterdisciplinary Center for Complex Systems, University of Bonn, Germany |
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Abstract: | To improve the estimation of drift and diffusion coefficients of stochastic processes in case of a limited amount of usable data due to e.g. non-stationarity of natural systems we suggest to use kernel-based instead of histogram-based regression. We propose a method for bandwidth selection and compare it to a widely used cross-validation method. Kernel-based regression reveals an enhanced ability to estimate drift and diffusion especially for a small amount of data. This allows one to improve resolvability of changes in complex dynamical systems as evidenced by an exemplary analysis of electroencephalographic data recorded from a human epileptic brain. |
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Keywords: | Fokker– Planck Kernel-based regression Bandwidth selection Epilepsy |
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