We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equations driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an estimator of the Hurst parameter, the diffusion parameter and the drift, which lies in a parametrised family of coercive drift coefficients. Our procedure is based on the assumption that the stationary distribution of the SDE and of its increments permits to identify the parameters of the model. Under this assumption, we prove consistency results and derive a rate of convergence for the estimator. Finally, we show that the identifiability assumption is satisfied in the case of a family of fractional Ornstein-Uhlenbeck processes and illustrate our results with some numerical experiments.

翻译：我们研究了由加性分数布朗运动驱动的随机微分方程中多个参数的联合统计估计问题。基于模型的离散时间观测，我们构造了赫斯特参数、扩散参数以及漂移项的估计量，其中漂移项属于一个满足强制条件的参数化漂移系数族。我们的方法基于以下假设：该随机微分方程及其增量的平稳分布能够唯一确定模型参数。在此假设下，我们证明了估计量的一致性结果，并推导出其收敛速率。最后，我们证明在分数奥恩斯坦-乌伦贝克过程族中该可辨识性假设成立，并通过数值实验验证了我们的结果。