Maximum likelihood estimation of drift and diffusion functions

The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [D. Kleinhans, R. Friedrich, A. Nawroth, J. Peinke, Phys. Lett. A 346 (2005) 42] and put the application of the method on a firm theoretical basis.