Finite sampling interval effects in Kramers-Moyal analysis

Abstract

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, can estimate these finite-time effects. For the first time, exact finite-time effects are described analytically for special cases; biologically inspired numerical examples are also worked through numerically. The approach developed here 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.