论文标题
混合分数Vasice工艺的最大似然估计
Maximum likelihood estimation for mixed fractional Vasicek processes
论文作者
论文摘要
混合分数Vasicek模型是传统Vasicek模型的扩展模型，已广泛用于建模波动率，利率和汇率。显然，如果某些现象是通过混合分数Vasick模型建模的，那么对此过程的统计推断引起了极大的兴趣。基于连续的时间观察，本文考虑了估计混合分数Vasicek模型中漂移参数的问题。我们将提出混合分数Vasicek模型中漂移参数的最大似然估计值，该模型具有radon-nikodym衍生物，用于混合分数布朗尼运动。使用基本的Martingale和Laplace变换，已经确定了所有$ h \ in（0,1）$，$ H \ neq 1/2 $的强大一致性和最大似然估计器的渐近态性。
The mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model, has been widely used in modelling volatility, interest rate and exchange rate. Obviously, if some phenomenon are modeled by the mixed fractional Vasicek model, statistical inference for this process is of great interest. Based on continuous time observations, this paper considers the problem of estimating the drift parameters in the mixed fractional Vasicek model. We will propose the maximum likelihood estimators of the drift parameters in the mixed fractional Vasicek model with the Radon-Nikodym derivative for a mixed fractional Brownian motion. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators have been established for all $H\in(0,1)$, $H\neq 1/2$.
