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

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].

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

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.

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.

scholarly journals Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters

2021 ◽  
Vol 6 (11) ◽  
pp. 12780-12794
Author(s):  
Abdulaziz Alsenafi ◽  
◽  
Mishari Al-Foraih ◽  
Khalifa Es-Sebaiy
Keyword(s):  
Least Squares ◽  
Continuous Time ◽  
Strong Consistency ◽  
Least Square ◽  
Uhlenbeck Process ◽  
Type Method ◽  
Ornstein Uhlenbeck Process ◽  
Discrete Time Observations ◽  
Theoretical Results ◽  
Drift Parameter

<abstract><p>Let $ B^{a, b}: = \{B_t^{a, b}, t\geq0\} $ be a weighted fractional Brownian motion of parameters $ a &gt; -1 $, $ |b| &lt; 1 $, $ |b| &lt; a+1 $. We consider a least square-type method to estimate the drift parameter $ \theta &gt; 0 $ of the weighted fractional Ornstein-Uhlenbeck process $ X: = \{X_t, t\geq0\} $ defined by $ X_0 = 0; \ dX_t = \theta X_tdt+dB_t^{a, b} $. In this work, we provide least squares-type estimators for $ \theta $ based continuous-time and discrete-time observations of $ X $. The strong consistency and the asymptotic behavior in distribution of the estimators are studied for all $ (a, b) $ such that $ a &gt; -1 $, $ |b| &lt; 1 $, $ |b| &lt; a+1 $. Here we extend the results of <sup>[<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>]</sup> (resp. <sup>[<xref ref-type="bibr" rid="b3">3</xref>]</sup>), where the strong consistency and the asymptotic distribution of the estimators are proved for $ -\frac12 &lt; a &lt; 0 $, $ -a &lt; b &lt; a+1 $ (resp. $ -1 &lt; a &lt; 0 $, $ -a &lt; b &lt; a+1 $). Simulations are performed to illustrate the theoretical results.</p></abstract>

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