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.

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 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].

Sequential Maximum Likelihood Estimation for the Parameter of the Linear Drift Term of the Rayleigh Diffusion Process

2015 ◽  
Vol 16 (1) ◽  
pp. 35-41
Author(s):  
Nenghui Kuang ◽  
Chunli Li ◽  
Huantian Xie
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Diffusion Process ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Linear Drift ◽  
Drift Term ◽  
Strongly Consistent ◽  
Drift Parameter

AbstractIn this paper, we investigate the properties of a sequential maximum likelihood estimator of the unknown linear drift parameter for the Rayleigh diffusion process. The estimator is shown to be closed, unbiased, normally distributed and strongly consistent. Finally a simulation study is presented to illustrate the efficiency of the estimator.

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
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