Sharp Large Deviations for the Fractional Ornstein–Uhlenbeck Process

Bernard Bercu, Laure Coutin, Nicolas Savy

Type: Article

Publication Date: 2011-11-10

Citations: 55

DOI: https://doi.org/10.1137/s0040585x97985108

Abstract

We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein–Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half.

Locations

Theory of Probability and Its Applications - View
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Sharp large deviations for the fractional Ornstein - Uhlenbeck process	2010	Bernard Bercu Bernard Bercu Laure Coutin Laure Coutin Nicolas Savy Nicolas Savy
+	Sharp Large Deviations for the Ornstein--Uhlenbeck Process	2002	Bernard Bercu Alain Rouault
+	Sharp large deviations for the non-stationary Ornstein–Uhlenbeck process	2012	Bernard Bercu Laure Coutin Nicolas Savy
+	Moderate deviations for parameter estimators in fractional Ornstein-Uhlenbeck process	2010	Gao Fu-qing Jiang Hui Baobin Wang
+	Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process	2011	Bernard Bercu Laure Coutin Nicolas Savy
+	Sharp large deviations for the non-stationary Ornstein-Uhlenbeck process	2011	Bernard Bercu Laure Coutin Nicolas Savy
+ PDF Chat	LARGE DEVIATION PROBABILITIES FOR MAXIMUM LIKELIHOOD ESTIMATOR AND BAYES ESTIMATOR OF A PARAMETER FOR MIXED FRACTIONAL ORNSTEIN-UHLENBECK TYPE PROCESS	2017	Μ. N. Mishra Bhagavatula Lakshmi Surya Prakasa Rao
+	A large deviation result for maximum likelihood estimator of non-homogeneous Ornstein–Uhlenbeck processes	2020	Shoujiang Zhao Qiaojing Liu
+	LARGE DEVIATIONS FOR PARAMETER ESTIMATE IN FRACTIONAL ORNSTEIN-UHLENBECK MODEL	2006	Gao Fu-qing
+	Moderate Deviations for Parameter Estimation in the Fractional Ornstein-Uhlenbeck Processes with Periodic Mean	2023	Hui Jiang Shimin Li Wei Gang Wang
+	Hypothesis testing of the drift parameter sign for fractional Ornstein-Uhlenbeck process	2016	Alexander Kukush Yuliya Mishura Kostiantyn Ralchenko
+	Hypothesis testing of the drift parameter sign for fractional Ornstein-Uhlenbeck process	2016	Alexander Kukush Yuliya Mishura Kostiantyn Ralchenko
+	Maximum likelihood estimation for the non-ergodic fractional Ornstein–Uhlenbeck process	2014	Katsuto Tanaka
+ PDF Chat	Estimation of all parameters in the fractional Ornstein–Uhlenbeck model under discrete observations	2021	El Mehdi Haress Yaozhong Hu
+	Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package	2011	Alexandre Brouste‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌ Stefano M. Iacus
+	Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package	2011	Alexandre Brouste‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌ Stefano M. Iacus
+ PDF Chat	Large deviations for drift parameter estimator of mixed fractional Ornstein–Uhlenbeck process	2016	Dmytro Marushkevych
+	Large deviations in testing fractional Ornstein–Uhlenbeck models	2007	Jaya P. N. Bishwal
+ PDF Chat	Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein–Uhlenbeck process	2013	Katsuto Tanaka
+	Estimation Of all parameters in the Fractional Ornstein-Uhlenbeck model under discrete observations	2020	El Mehdi Haress Yaozhong Hu

Works That Cite This (46)

Action	Title	Year	Authors
+ PDF Chat	Berry-Esséen bound for the parameter estimation of fractional Ornstein-Uhlenbeck processes with the hurst parameter H∈(0,12)	2019	Yong Chen Ying Li
+ PDF Chat	Berry–Esséen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes	2019	Yong Chen Nenghui Kuang Ying Li
+	LAN property for stochastic differential equations driven by fractional Brownian motion of Hurst parameter $H\in(1/4,1/2)$	2018	Kohei Chiba
+	Berry-Esseen bound for the Parameter Estimation of Fractional Ornstein-Uhlenbeck Processes	2018	Yong Chen Nenghui Kuang Ying Li
+	Moderate deviation for parameter estimator in the stochastic parabolic equations with additive fractional Brownian motion	2013	Jiang Hui
+	Precise asymptotics for large deviations of integral forms	2012	Xiangfeng Yang
+	Sharp large deviations for the non-stationary Ornstein–Uhlenbeck process	2012	Bernard Bercu Laure Coutin Nicolas Savy
+ PDF Chat	Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package	2012	Alexandre Brouste‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌ Stefano M. Iacus
+	Self-normalized asymptotic properties for the parameter estimation in fractional Ornstein–Uhlenbeck process	2018	Hui Jiang Junfeng Liu Shaochen Wang
+	Two examples of non strictly convex large deviations	2016	Stefano De Marco Antoine Jacquier Patrick Roome

Works Cited by This (8)

Action	Title	Year	Authors
+	Sharp Large Deviations for the Ornstein--Uhlenbeck Process	2002	Bernard Bercu Alain Rouault
+	Asymptotic properties of MLE for partially observed fractional diffusion system	2009	Alexandre Brouste‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌ Marina Kleptsyna
+	A functional large deviations principle for quadratic forms of Gaussian stationary processes	1999	Fabrice Gamboa Alain Rouault Marguerite Zani
+ PDF Chat	Parameter estimation for fractional Ornstein–Uhlenbeck processes	2010	Yaozhong Hu David Nualart
+	Large deviations for quadratic forms of stationary Gaussian processes	1997	Bernard Bercu Fabrice Gamboa Alain Rouault
+	Large deviations in testing fractional Ornstein–Uhlenbeck models	2007	Jaya P. N. Bishwal
+ PDF Chat	On Deviations of the Sample Mean	1960	R. R. Bahadur Rema Rao
+	None	1997	Włodzimierz Bryc Amir Dembo