Optimal estimation of the local time and the occupation time measure for an α-stable Lévy process

被引：0
|
作者：
Amorino, Chiara [1 ]
Jaramillo, Arturo [2 ]
Podolskij, Mark [1 ]
机构：
[1] Univ Luxembourg, Dept Math, 6 Ave Fonte, L-4364 Esch Sur Alzette, Luxembourg
[2] Res Math CIMAT, Jalisco S-N, Valenciana 36023, Guanajuato, Mexico
来源：
MODERN STOCHASTICS-THEORY AND APPLICATIONS | 2024年 / 11卷 / 02期
基金：
欧洲研究理事会;
关键词：
High frequency data; local time; mixed normal distribution; occupation time; stable Levy processes; CONTINUITY; CONVERGENCE; INCREMENTS; LIMIT;
D O I：
10.15559/24-VMSTA243
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
A novel theoretical result on estimation of the local time and the occupation time measure of an alpha-stable Levy process with alpha is an element of (1, 2) is presented. The approach is based upon computing the conditional expectation of the desired quantities given high frequency data, which is an L2-optimal statistic by construction. The corresponding stable central limit theorems are proved and a statistical application is discussed. In particular, this work extends the results of [20], which investigated the case of the Brownian motion.
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页码：149 / 168
页数：20
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