Drift parameter estimation for infinite-dimensional fractional Ornstein-Uhlenbeck process

被引：12

作者：

Maslowski, Bohdan ^{[1
]}

Tudor, Ciprian A. ^{[2
,3
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Prague 18675 8, Czech Republic

[2] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[3] Acad Econ Studies, Dept Math CCMAFA, Bucharest, Romania

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2013年 / 137卷 / 07期

关键词：

Fractional Brownian motion; Parameter estimation; Stochastic evolution equations; Malliavin calculus; Multiple Wiener-Ito integrals; Strong consistency; Asymptotic normality; ASYMPTOTIC PROPERTIES; INTEGRALS;

D O I：

10.1016/j.bulsci.2013.04.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the least squares estimator for the drift parameter of an infinite-dimensional fractional Ornstein-Uhlenbeck process with Hurst parameter H >= 1/2 This estimator can be expressed in terms of a divergence integral with respect to the fractional Brownian motion. Using some recently developed criteria based on Malliavin calculus and Wiener-Ito chaos expansion, we prove the strong consistency and the asymptotic normality of the estimator. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：880 / 901

页数：22

共 50 条

[1] Ergodicity and Drift Parameter Estimation for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process of the Second Kind
Balde, Maoudo Faramba
Es-Sebaiy, Khalifa
Tudor, Ciprian A.
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2020, 81 (03): : 785 - 814
[2] Ergodicity and parameter estimates for infinite-dimensional fractional Ornstein-Uhlenbeck process
Maslowski, Bohdan
Pospisil, Jan
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 2008, 57 (03): : 401 - 429
[3] Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process
Bohdan Maslowski
Jan Pospíšil
[J]. Applied Mathematics and Optimization, 2008, 57 : 401 - 429
[4] Ergodicity and Drift Parameter Estimation for Infinite-Dimensional Fractional Ornstein–Uhlenbeck Process of the Second Kind
Maoudo Faramba Balde
Khalifa Es-Sebaiy
Ciprian A. Tudor
[J]. Applied Mathematics & Optimization, 2020, 81 : 785 - 814
[5] Drift parameter estimation for fractional Ornstein-Uhlenbeck process of the second kind
Azmoodeh, Ehsan
Morlanes, Jose Igor
[J]. STATISTICS, 2015, 49 (01) : 1 - 18
[6] On parameter estimation of fractional Ornstein-Uhlenbeck process
Farah, Fatima-Ezzahra
[J]. RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2022, 30 (03) : 161 - 170
[7] Representation of a fractional Brownian motion in terms of an infinite-dimensional Ornstein-Uhlenbeck process
Muravlev, A. A.
[J]. RUSSIAN MATHEMATICAL SURVEYS, 2011, 66 (02) : 439 - 441
[8] On drift parameter estimation for reflected fractional Ornstein-Uhlenbeck processes
Lee, Chihoon
Song, Jian
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2016, 88 (05) : 751 - 778
[9] Hypothesis testing of the drift parameter sign for fractional Ornstein-Uhlenbeck process
Kukush, Alexander
Mishura, Yuliya
Ralchenko, Kostiantyn
[J]. ELECTRONIC JOURNAL OF STATISTICS, 2017, 11 (01): : 385 - 400
[10] Parameter estimation for fractional Ornstein-Uhlenbeck processes
Hu, Yaozhong
Nualart, David
[J]. STATISTICS & PROBABILITY LETTERS, 2010, 80 (11-12) : 1030 - 1038

← 1 2 3 4 5 →