| 讲座简介： | Abstract: In this talk I will present some recent results on the parameter estimation problems for the Ornstein-Uhlenbeck processes determined by the linear stochastic differential equation driven by the simplest long memory process: $dX_t=-\theta X_tdt +\sigma dB_t$, where $B_t$ is fractional Brownian motion of Hurst parameter $H$. Assume that the parameter $\theta$ is unknown and the process $X_t$ is observable. We want to estimate $\theta$ from the observation $X_t$. The asymptotic consistency of the estimators as well as the central limit type theorem, convergence in density and so on will be presented. The observations can be continuous time or discrete time. |
