Parametric estimation in the Vasicek-type model driven by sub-fractional Brownian motion (Q1712059)

Summary: In the paper, we tackle the least squares estimators of the Vasicek-type model driven by sub-fractional Brownian motion: \[ d X_t = (\mu + \theta X_t) d t + d S_t^H,\quad t \geq 0 \] with \(X_0 = 0\), where \(S^H\) is a sub-fractional Brownian motion whose Hurst index \(H\) is greater than \(\frac{1}{2}\), and \(\mu \in \mathbb R\), \(\theta \in \mathbb R^+\) are two unknown parameters. Based on the so-called continuous observations, we suggest the least square estimators of \(\mu\) and \(\theta\) and discuss the consistency and asymptotic distributions of the two estimators.