scholarly journals Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein–Uhlenbeck process

2013 ◽  
Vol 16 (3) ◽  
pp. 173-192 ◽  
Author(s):  
Katsuto Tanaka
Keyword(s):  
Maximum Likelihood ◽  
Uhlenbeck Process ◽  
Minimum Contrast ◽  
Ornstein Uhlenbeck Process

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

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 Large deviations for the Ornstein-Uhlenbeck process with shift

2015 ◽  
Vol 47 (03) ◽  
pp. 880-901 ◽  
Author(s):  
Bernard Bercu ◽  
Adrien Richou
Keyword(s):  
Maximum Likelihood ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Shift Parameter ◽  
Uhlenbeck Process ◽  
Deviation Principle ◽  
Large Deviation Principles ◽  
Ornstein Uhlenbeck Process

We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck process with shift. We propose a new approach to establish large deviation principles which allows us, via a suitable transformation, to circumvent the classical nonsteepness problem. We estimate simultaneously the drift and shift parameters. On the one hand, we prove a large deviation principle for the maximum likelihood estimates of the drift and shift parameters. Surprisingly, we find that the drift estimator shares the same large deviation principle as the estimator previously established for the Ornstein-Uhlenbeck process without shift. Sharp large deviation principles are also provided. On the other hand, we show that the maximum likelihood estimator of the shift parameter satisfies a large deviation principle with a very unusual implicit rate function.

scholarly journals Large deviations for the Ornstein-Uhlenbeck process with shift

2015 ◽  
Vol 47 (3) ◽  
pp. 880-901 ◽  
Author(s):  
Bernard Bercu ◽  
Adrien Richou
Keyword(s):  
Maximum Likelihood ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Shift Parameter ◽  
Uhlenbeck Process ◽  
Deviation Principle ◽  
Large Deviation Principles ◽  
Ornstein Uhlenbeck Process

We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck process with shift. We propose a new approach to establish large deviation principles which allows us, via a suitable transformation, to circumvent the classical nonsteepness problem. We estimate simultaneously the drift and shift parameters. On the one hand, we prove a large deviation principle for the maximum likelihood estimates of the drift and shift parameters. Surprisingly, we find that the drift estimator shares the same large deviation principle as the estimator previously established for the Ornstein-Uhlenbeck process without shift. Sharp large deviation principles are also provided. On the other hand, we show that the maximum likelihood estimator of the shift parameter satisfies a large deviation principle with a very unusual implicit rate function.

Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: Continuous and discrete sampling

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Jaya Bishwal
Keyword(s):  
Normal Distribution ◽  
Hurst Exponent ◽  
Standard Normal Distribution ◽  
Discrete Observations ◽  
Uhlenbeck Process ◽  
Minimum Contrast ◽  
Contrast Estimation ◽  
Ornstein Uhlenbeck Process ◽  
Standard Normal ◽  
Drift Parameter

AbstractThe paper shows that the distribution of the normalized minimum contrast estimator of the drift parameter in the fractional Ornstein-Uhlenbeck process observed over [0, T] converges to the standard normal distribution with an uniform error rate of the order O(T −1/2) for the case H > 1/2 where H is the Hurst exponent of the fractional Brownian motion driving the Ornstein-Uhlenbeck process. Then based on discrete observations, it introduces several approximate minimum contrast estimators and studies their rate of of weak convergence to normal distribution.

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