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 non-parametric. 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.
翻译:我们得出一致性和无症状的正常性结果,以获得在连续连续时间环境中在离散时间里观察到的异形随机过程漂移参数的准最大可能性方法,我们分析的特别特征是,异形组成部分是没有观测的,而不是参数。此外,这种漂移可能取决于(已知和未观测的)异形异形。我们的结果显示,异形半参数扩散和后向的SDEs。模拟研究证实,所提议的方法产生了良好的趋同结果。