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We derive consistency and asymptotic normality results for quasi-maximumlikelihood methods for drift parameters of ergodic stochastic processesobserved in discrete time in an underlying continuous-time setting. The specialfeature of our analysis is that the stochastic integral part is unobserved andnon-parametric. Additionally, the drift may depend on the (unknown andunobserved) stochastic integrand. Our results hold for ergodic semi-parametricdiffusions and backward SDEs. Simulation studies confirm that the methodsproposed yield good convergence results.

Efficient drift parameter estimation for ergodic solutions of backward SDEs