Asymptotic behavior of weighted quadratic variation of tempered fractional Brownian motion

被引：0
|
作者：
Wang, Jixia [1 ]
Sun, Lu [1 ]
Miao, Yu [1 ]
机构：
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
来源：
STATISTICS & PROBABILITY LETTERS | 2024年 / 207卷
基金：
中国国家自然科学基金;
关键词：
Tempered fractional Brownian motion; Weighted quadratic variation; Malliavin calculus; POWER VARIATIONS; SCHEMES;
D O I：
10.1016/j.spl.2023.110020
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：
This paper investigates the convergence in L-2 of renormalized weighted quadratic variation associated to tempered fractional Brownian motion with Hurst index 0 < H < 1/4 and lambda > 0. We first give four lemmas about tempered fractional Brownian motion by means of Malliavin calculus. Then the convergence for tempered fractional Brownian motion is derived in L-2 through these lemmas. Our main result extends findings of Nourdin (2008), concerning the weighted power variations of fractional Brownian motion.
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