Variations and estimators for self-similarity parameter of sub-fractional Brownian motion via Malliavin calculus

被引：3

作者：

Liu, Junfeng ^{[1
]}

Tang, Donglei ^{[2
]}

Cang, Yuquan ^{[1
]}

机构：

[1] Nanjing Audit Univ, Dept Stat, Nanjing, Jiangsu, Peoples R China

[2] Nanjing Audit Univ, Dept Math, Nanjing, Jiangsu, Peoples R China

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2017年 / 46卷 / 07期

基金：

中国博士后科学基金;

关键词：

Subfractional Brownian motion; multiple stochastic integral; Malliavin calculus; quadratic variation; selfsimilarity; statistical estimation; MULTIPLE STOCHASTIC INTEGRALS; CENTRAL LIMIT-THEOREMS; RESPECT; SYSTEMS; TIME;

D O I：

10.1080/03610926.2013.819923

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：

Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of the adjusted quadratic variation for a sub-fractional Brownian motion. We apply our results to construct strongly consistent statistical estimators for the self-similarity of sub-fractional Brownian motion.

引用

页码：3276 / 3289

页数：14

共 50 条

[41] Parameter Estimation for Ornstein-Uhlenbeck Process Driven by Sub-fractional Brownian Processes
School of Mathematics and Statistics, An’yang Normal University, An’yang
455000, China
不详
455000, China
IAENG Int. J. Appl. Math., 2
[42] Hedging lookback-barrier option by Malliavin calculus in a mixed fractional Brownian motion environment
Liu, Kefan
Zhang, Jichao
Yang, Yueting
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2024, 133
[43] Nonparametric estimation of trend for stochastic differential equations driven by sub-fractional Brownian motion
Rao, B. L. S. Prakasa
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2020, 28 (02) : 113 - 122
[44] Parametric Estimation in the Vasicek-Type Model Driven by Sub-Fractional Brownian Motion
Li, Shengfeng
Dong, Yi
ALGORITHMS, 2018, 11 (12):
[45] Asymptotics of Karhunen-Loeve Eigenvalues for Sub-Fractional Brownian Motion and Its Application
Cai, Chun-Hao
Hu, Jun-Qi
Wang, Ying-Li
FRACTAL AND FRACTIONAL, 2021, 5 (04)
[46] European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time
Guo, Zhidong
Liu, Yang
Dai, Linsong
FRACTAL AND FRACTIONAL, 2024, 8 (01)
[47] An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion
Jafari, Hossein
Farahani, Hamed
STOCHASTICS AND DYNAMICS, 2023, 23 (03)
[48] Mixed Sub-fractional Brownian Motion and Drift Estimation of Related Ornstein–Uhlenbeck Process
Chunhao Cai
Qinghua Wang
Weilin Xiao
Communications in Mathematics and Statistics, 2023, 11 : 229 - 255
[49] Riemann-Liouville fractional stochastic evolution equations driven by mixed sub-fractional Brownian motion
Boutlilis, Mokhtaria
Kandouci, Abdeldjebbar
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2025, 33 (01) : 87 - 97
[50] Asymptotic Normality of Parameter Estimators for Mixed Fractional Brownian Motion with Trend
Ralchenko, Kostiantyn
Yakovliev, Mykyta
AUSTRIAN JOURNAL OF STATISTICS, 2023, 52 : 127 - 148

← 1 2 3 4 5 →