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Finite sampling interval effects in Kramers-Moyal analysis. (English) Zbl 1233.82033

Summary: Large sampling intervals can affect reconstruction of Kramers-Moyal coefficients from data. A new method, which is direct, non-stochastic and exact up to numerical accuracy, is developed to estimate these finite time effects. The method is applied numerically to biologically inspired examples. Exact finite time effects are also described analytically for two special cases. The approach developed will permit better evaluation of Langevin or Fokker-Planck based models from data with large sampling intervals. It can also be used to predict the sampling intervals for which finite time effects become significant.

MSC:

82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
37M10 Time series analysis of dynamical systems
82C70 Transport processes in time-dependent statistical mechanics
92C40 Biochemistry, molecular biology
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