Optimal L2-approximation of occupation and local times for symmetric stable processes

被引：1

作者：

Altmeyer, Randolf ^{[1
]}

Le Guevel, Ronan ^{[2
]}

机构：

[1] Univ Cambridge, Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WB, England

[2] Univ Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes, France

来源：

ELECTRONIC JOURNAL OF STATISTICS | 2022年 / 16卷 / 01期

关键词：

Occupation time; local time; stable process; Levy process; lower bound; DENSITY-ESTIMATION; APPROXIMATION; CONVERGENCE; RATES;

D O I：

10.1214/22-EJS2013

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：

The L-2-approximation of occupation and local times of a symmetric alpha-stable Levy process from high frequency discrete time observations is studied. The standard Riemann sum estimators are shown to be asymptotically efficient when 0 < alpha <= 1, but only rate optimal for 1 < alpha <= 2. For this, the exact convergence of the L-2-approximation error is proven with explicit constants.

引用

页码：2859 / 2883

页数：25

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