title: Fokker-Planck perspective on stochastic delay systems: exact solutions and data analysis of biological systems.
abstract: Stochastic delay systems with additive noise are examined from the perspective of Fokker-Planck equations. For a linear system, the exact stationary probability density is derived by means of a delay Fokker-Planck equation. We show how to determine the delay equation of the linear system from experimental data, and corroborate a fundamental result previously obtained by Küchler and Mensch. We also propose a method to derive delay equations of nonlinear systems from experimental data. To this end, the theory of multivariate Fokker-Planck equations is used. The applicability of this method is demonstrated for stochastic models describing tracking and pointing movements of humans.
authors.affiliation: Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.
authors.forename: T D
authors.initials: TD
authors.lastname: Frank
authors.forename: P J
authors.initials: PJ
authors.lastname: Beek
authors.forename: R
authors.initials: R
authors.lastname: Friedrich
mesh_terms: D055592:Biophysical Phenomena; D001703:Biophysics; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D009068:Movement; D015999:Multivariate Analysis; D013223:Statistics as Topic; D013269:Stochastic Processes