  The Kramers-Moyal analysis is a well established approach to analyze
stochastic time series from complex systems. If the sampling interval of a
measured time series is too low, systematic errors occur in the analysis
results. These errors are labeled as finite time effects in the literature. In
the present article, we present some new insights about these effects and
discuss the limitations of a previously published method to estimate
Kramers-Moyal coefficients at the presence of finite time effects. To increase
the reliability of this method and to avoid misinterpretations, we extend it by
the computation of error estimates for estimated parameters using a Monte Carlo
error propagation technique. Finally, the extended method is applied to a data
set of an optical trapping experiment yielding estimations of the forces acting
on a Brownian particle trapped by optical tweezers. We find an increased
Markov-Einstein time scale of the order of the relaxation time of the process
which can be traced back to memory effects caused by the interaction of the
particle and the fluid. Above the Markov-Einstein time scale, the process can
be very well described by the classical overdamped Markov model for Brownian
motion.
