Maximum likelihood estimation in the non-ergodic fractional Vasicek model

We investigate the fractional Vasicek model described by the stochastic differential equation $dX_t=(α-βX_t)\,dt+γ\,dB^H_t$, $X_0=x_0$, driven by the fractional Brownian motion $B^H$ with the known Hurst parameter $H\in (1/2,1)$. We study the maximum likelihood estimators for unknown parameters $α$ and $β$ in the non-ergodic case (when $β<0$) for arbitrary $x_0\in \mathbb{R}$, generalizing the result of Tanaka, Xiao and Yu (2019) for particular $x_0=α/β$, derive their asymptotic distributions and prove their asymptotic independence.

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