On the definition and handling of different drift and diffusion estimates

A previously devised approach for the reconstruction of Langevin processes from given data is revised with respect to disturbances stemming from finite sampling rates and the presence of external measurement noise. For these two cases and a combination of both three different estimates for the drift and diffusion functions are introduced, and an optimization procedure is presented that allows the reconstruction of the intrinsic functions from these estimates. Special attention is paid to the reconstruction of deterministic fixed points defining the characteristic behaviour of a process, and its robustness against the considered disturbing effects.