Estimating Kramers–Moyal coefficients in short and non-stationary data sets

To reliably estimate the dynamics of diffusive Markov processes, we combine statistically independent empirical data. Since commutative statistics do not affect fundamental Markov properties, they provide robust estimators for Kramers–Moyal coefficients even when registration time and sampling frequency of individual recordings are rather limited. We also show how the results of the method can be further improved and extended in order to apply it in the non-stationary regime.