The rate of convergence of Hurst index estimate for the stochastic differential equation

被引：19

作者：

Kubilius, K. ^{[1
]}

Mishura, Y. ^{[2
]}

机构：

[1] Vilniaus Univ, Inst Math & Informat, LT-08663 Vilnius, Lithuania

[2] Natl Taras Shevchenko Kyiv Univ, UA-01601 Kiev, Ukraine

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2012年 / 122卷 / 11期

关键词：

Fractional Brownian motion; Stochastic differential equation; First- and second-order quadratic variations; Estimates of Hurst parameter; Rate of convergence; INEQUALITY; DRIVEN;

D O I：

10.1016/j.spa.2012.06.011

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：

We consider a stochastic differential equation involving a pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed values of the solution. The rate of convergence of these estimates to the true value of a parameter is established when the diameter of interval partition tends to zero. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：3718 / 3739

页数：22

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