Finite sampling interval effects in Kramers-Moyal analysis

TL;DR

This paper introduces a new exact method to analyze and correct the effects of large sampling intervals on the estimation of Kramers-Moyal coefficients, improving model evaluation from data with coarse sampling.

Contribution

A novel direct and exact approach is developed to quantify finite-time effects in Kramers-Moyal analysis, including analytical descriptions for specific cases and numerical examples.

Findings

Exact finite-time effects are analytically described for certain cases.

The new method accurately estimates finite-time effects up to numerical precision.

The approach enables better evaluation of Langevin and Fokker-Planck models from coarse data.

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.