论文标题
最佳估计一些随机数量的Lévy过程
Optimal estimation of some random quantities of a Lévy process
论文作者
论文摘要
在本文中，我们根据莱维过程的高频观察结果对某些随机数量的最佳估计提出了新的理论结果。更具体地说，我们研究了线性布朗运动和稳定的莱维过程的条件平均值和条件中值估计值的渐近理论。我们文章的另一个贡献是对当地时间的条件均值估计以及线性布朗运动的职业时间度量。我们证明，与经典估计器相比，新的估计器效率要高得多。此外，我们讨论了基础模型参数的预估计，这是拟议统计的实际实施所必需的。
In this paper we present new theoretical results on optimal estimation of certain random quantities based on high frequency observations of a Lévy process. More specifically, we investigate the asymptotic theory for the conditional mean and conditional median estimators of the supremum/infimum of a linear Brownian motion and a stable Lévy process. Another contribution of our article is the conditional mean estimation of the local time and the occupation time measure of a linear Brownian motion. We demonstrate that the new estimators are considerably more efficient compared to the classical estimators. Furthermore, we discuss pre-estimation of the parameters of the underlying models, which is required for practical implementation of the proposed statistics.
