ABSTRACT There is considerable interest in parameter estimation in Lévy models. The maximum likelihood estimator is widely used because under certain conditions it enjoys asymptotic efficiency properties. The toolkit for Lévy processes is the local asymptotic normality which guarantees these conditions. Although the likelihood function is not known explicitly, we prove local asymptotic normality for the location and scale parameters of the Student-Lévy process assuming high-frequency data. In addition, we propose a numerical method to make maximum likelihood estimates feasible based on the Monte Carlo expectation-maximization algorithm. A simulation study verifies the theoretical results.

中文翻译：

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高频采样下 Student-Lévy 过程的局部渐近正态性

摘要人们对 Lévy 模型中的参数估计非常感兴趣。最大似然估计器被广泛使用，因为在某些条件下它具有渐近效率特性。Lévy 过程的工具包是保证这些条件的局部渐近正态性。尽管似然函数未知，但我们证明了假设高频数据的 Student-Lévy 过程的位置和尺度参数的局部渐近正态性。此外，我们提出了一种基于蒙特卡罗期望最大化算法的数值方法，使最大似然估计可行。模拟研究验证了理论结果。