Asymptotic distribution of the maximum likelihood estimator in the fractional Vašíček model
Анотація
The fractional VaÅ¡ÃÄek model \begin{equation*} dX_t = \left (\alpha - \beta X_t \right ) dt + \gamma dB_t^H \end{equation*} is considered. The model is driven by the fractional Brownian motion $B^H$ with the Hurst index $H\in \bigl (\frac 12,1\bigr )$. The asymptotic distribution of the maximum likelihood estimator is studied for the vector parameter $(\alpha , \beta )$. It is proved that this estimator is asymptotically normal in the case of $\beta >0$. It is shown that the estimators of the parameters $\alpha$ and $\beta$ are asymptotically independent.
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