scholarly journals Consistency of the drift parameter estimator for the discretized fractional Ornstein–Uhlenbeck process with Hurst index $H\in(0,\frac{1}{2})$

2015 ◽  
Vol 9 (2) ◽  
pp. 1799-1825 ◽  
Author(s):  
Kęstutis Kubilius ◽  
Yuliya Mishura ◽  
Kostiantyn Ralchenko ◽  
Oleg Seleznjev
Keyword(s):  
Hurst Index ◽  
Parameter Estimator ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

scholarly journals Berry–Esséen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes

2019 ◽  
Vol 20 (04) ◽  
pp. 2050023 ◽  
Author(s):  
Yong Chen ◽  
Nenghui Kuang ◽  
Ying Li
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Continuous Time ◽  
Index Formula ◽  
Hurst Index ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Time Observation ◽  
Statistical Estimations ◽  
Drift Parameter

For an Ornstein–Uhlenbeck process driven by fractional Brownian motion with Hurst index [Formula: see text], we show the Berry–Esséen bound of the least squares estimator of the drift parameter based on the continuous-time observation. We use an approach based on Malliavin calculus given by Kim and Park [Optimal Berry–Esséen bound for statistical estimations and its application to SPDE, J. Multivariate Anal. 155 (2017) 284–304].

Berry-Esseen bounds and ASCLTs for drift parameter estimator of mixed fractional Ornstein-Uhlenbeck process with discrete observations

2019 ◽  
Vol 64 (3) ◽  
pp. 502-525
Author(s):  
Farez Alazemi ◽  
Farez Alazemi ◽  
Soukhana Douissi ◽  
Soukhana Douissi ◽  
Khalifa Es-Sebaiy ◽  
...  
Keyword(s):  
Discrete Observations ◽  
Parameter Estimator ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

Рассматривается задача оценивания сноса смешанного процесса Орнштейна-Уленбека на основе наблюдений в фиксированные дискретные моменты времени. С использованием исчисления Маллявена и недавнего анализа Нурдина-Пеккати исследуется асимптотическое поведение оценки. Более точно, изучаются сильная состоятельность и асимптотическое распределение оценки; установлена также скорость ее сходимости по распределению для всех $H\in(0,1)$. Более того, доказано, что в случае $H\in(0,3/4]$ оценка удовлетворяет центральной предельной теореме для сходимости почти наверное.

Speed of Convergence of the Maximum Likelihood Estimator in the Ornstein-Uhlenbeck Process

1995 ◽  
Vol 45 (3-4) ◽  
pp. 245-252 ◽  
Author(s):  
J. P. N. Bishwal ◽  
Arup Bose
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Subject Classification ◽  
Speed Of Convergence ◽  
Primary 62F12 ◽  
Likelihood Estimator ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

Berry-Bsseen bounds with random norming and Jario deviation probabilities arc derived for the maximum likelihood estimator of the drift parameter in tho Ornstoin-Uhlenbeck proccss. AMS (1991) Subject Classification: Primary 62F12, 62M05 Secondary 60FOS, 60F10

scholarly journals Hypothesis testing of the drift parameter sign for fractional Ornstein–Uhlenbeck process

2017 ◽  
Vol 11 (1) ◽  
pp. 385-400 ◽  
Author(s):  
Alexander Kukush ◽  
Yuliya Mishura ◽  
Kostiantyn Ralchenko
Keyword(s):  
Hypothesis Testing ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

CONTROLLED DRIFT ESTIMATION IN FRACTIONAL DIFFUSION LINEAR SYSTEMS

2013 ◽  
Vol 13 (03) ◽  
pp. 1250025 ◽  
Author(s):  
ALEXANDRE BROUSTE ◽  
CHUNHAO CAI
Keyword(s):  
Maximum Likelihood ◽  
Laplace Transform ◽  
Fractional Diffusion ◽  
Likelihood Estimator ◽  
Uhlenbeck Process ◽  
Drift Estimation ◽  
Partially Observed ◽  
Ornstein Uhlenbeck Process ◽  
Drift Parameter

This paper is devoted to the determination of the asymptotical optimal input for the estimation of the drift parameter in a partially observed but controlled fractional Ornstein–Uhlenbeck process. Large sample asymptotical properties of the Maximum Likelihood Estimator are deduced using Ibragimov–Khasminskii program and Laplace transform computations.

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