  Recently, several powerful tools for the reconstruction of stochastic
differential equations from measured data sets have been proposed [e.g. Siegert
et al., Physics Letters A 243, 275 (1998); Hurn et al., Journal of Time Series
Analysis 24, 45 (2003)]. Efficient application of the methods, however,
generally requires Markov properties to be fulfilled. This constraint typically
seems to be violated on small scales, which frequently is attributed to
physical effects. On the other hand, measurement noise such as uncorrelated
measurement and discretization errors has large impacts on the statistics of
measurements on small scales. We demonstrate, that the presence of measurement
noise, likewise, spoils Markov properties of an underlying Markov processes.
This fact is promising for the further development of techniques for the
reconstruction of stochastic processes from measured data, since limitations at
small scales might stem from artificial noise sources rather than from
intrinsic properties of the dynamics of the underlying process. Measurement
noise, however, can be controlled much better than the intrinsic dynamics of
the underlying process.

Data Analysis, Statistics and Probability