论文标题
最佳估计当地时间和职业时间度量
Optimal estimation of local time and occupation time measure for an α-stable Levy process
论文作者
论文摘要
我们提出了一个新的理论结果，以估计α-稳定的莱维过程的局部时间和占用时间度量（1，2）。我们的方法是基于计算给定高频数据的所需数量的条件期望，这是通过构造的l^2-最佳统计量。我们证明了相应的稳定中心限制定理并讨论统计应用。特别是，这项工作扩展了[Ivanovs和i podolskij（2021）]的结果，该结果调查了布朗运动的情况。
We present a novel theoretical result on estimation of local time and occupation time measure of an α-stable Lévy process with α in (1, 2). Our approach is based upon computing the conditional expectation of the desired quantities given high frequency data, which is an L^2-optimal statistic by construction. We prove the corresponding stable central limit theorems and discuss a statistical application. In particular, this work extends the results of [Ivanovs and i Podolskij (2021)], which investigated the case of the Brownian motion.
