This paper estimates the drift parameters in the fractional Vasicek model from a continuous record of observations via maximum likelihood (ML). The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the boundary case for the entire range of the Hurst parameter, providing a complete treatment of asymptotic analysis. It is shown that changing the sign of the persistence parameter changes the asymptotic theory for the MLE, including the rate of convergence and the limiting distribution. It is also found that the asymptotic theory depends on the value of the Hurst parameter.

中文翻译：

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分数Vasicek模型的最大似然估计

本文通过最大似然（ML）的连续观测记录估算了分数Vasicek模型中的漂移参数。在Hurst参数整个范围的平稳情况，爆炸情况和边界情况下，建立了ML估计（MLE）的渐近理论，从而提供了对渐进分析的完整处理。结果表明，改变持续参数的符号会改变MLE的渐近理论，包括收敛速度和极限分布。还发现渐近理论取决于赫斯特参数的值。