We derive consistency and asymptotic normality results for quasi‐maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous‐time setting. The special feature of our analysis is that the stochastic integral part is unobserved and nonparametric. Additionally, the drift may depend on the (unknown and unobserved) stochastic integrand. Our results hold for ergodic semi‐parametric diffusions and backward SDEs. Simulation studies confirm that the methods proposed yield good convergence results.

中文翻译：

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后向 SDE 遍历解的高效漂移参数估计

我们得出了准最大似然方法的一致性和渐近正态性结果，用于在基础连续时间设置中的离散时间中观察到的遍历随机过程的漂移参数。我们分析的特点是随机积分部分是不可观测的且非参数的。此外，漂移可能取决于（未知且未观察到的）随机被积函数。我们的结果适用于遍历半参数扩散和后向 SDE。仿真研究证实所提出的方法产生了良好的收敛结果。