  We study efficiency of non-parametric estimation of diffusions (stochastic
differential equations driven by Brownian motion) from long stationary
trajectories. First, we introduce estimators based on conditional expectation
which is motivated by the definition of drift and diffusion coefficients. These
estimators involve time- and space-discretization parameters for computing
expected values from discretely-sampled stationary data. Next, we analyze
consistency and mean squared error of these estimators depending on
computational parameters. We derive relationships between the number of
observational points, time- and space-discretization parameters in order to
achieve the optimal speed of convergence and minimize computational complexity.
We illustrate our approach with numerical simulations.
