Fokker-Planck perspective on stochastic delay systems: exact solutions and data analysis of biological systems.
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.
Frank
T D
TD
Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.
Beek
P J
PJ
Friedrich
R
R
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