Moderate deviations for parameter estimation in the fractional Ornstein-Uhlenbeck processes with periodic mean (Q6541371)

The paper considers the fractional Ornstein-Uhlenbeck process with periodic mean function \(d{X_t} = \left( {\sum\limits_{i = 1}^p {{\mu _i}{\varphi _i}(t)} - \alpha {X_t}} \right)dt + dB_t^H\), \({X_0} = 0\), where \({B^H} = \left\{ {\left. {B_t^H,t \ge 0} \right\}} \right.\) is a fractional Brownian motion with Hurst index \(H \in \left( {\frac{1}{2},1} \right)\), parameters \(\theta = {\left( {{\mu _1},\ldots,{\mu _p},\alpha } \right)^T}\) are all unknown, with \({\mu _i} \in R\), \(\alpha > 0\), \(i = 1,\ldots,p\). It investigates the asymptotic properties of the drift parameter estimators for the process under consideration.