Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift.
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Gao, Fuqing, Jiang, Hui (2009)
Electronic Communications in Probability [electronic only]
H. Hilden (1976)
Metrika
Arnaud Gloter, Jean Jacod (2001)
ESAIM: Probability and Statistics
We consider a diffusion process which is observed at times for , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance . There is an unknown parameter within the diffusion coefficient, to be estimated. In this first paper the case when is indeed a gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information. What is perhaps...
Arnaud Gloter, Jean Jacod (2010)
ESAIM: Probability and Statistics
We consider a diffusion process X which is observed at times i/n for i = 0,1,...,n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance pn. There is an unknown parameter within the diffusion coefficient, to be estimated. In this first paper the case when X is indeed a Gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information....
Arnaud Gloter, Jean Jacod (2001)
ESAIM: Probability and Statistics
We consider a diffusion process which is observed at times for , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance . There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process is a gaussian martingale, and we conjecture that they are also optimal in the general case.
Arnaud Gloter, Jean Jacod (2010)
ESAIM: Probability and Statistics
We consider a diffusion process X which is observed at times i/n for i = 0,1,...,n, each observation being subject to a measurement error. All errors are independent and centered Gaussian with known variance pn. There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process X is a Gaussian martingale, and we conjecture that they are also optimal in the general case.
Arnaud Gloter (2000)
ESAIM: Probability and Statistics
Arnaud Gloter (2010)
ESAIM: Probability and Statistics
Let (Xt) be a diffusion on the interval (l,r) and Δn a sequence of positive numbers tending to zero. We define Ji as the integral between iΔn and (i + 1)Δn of Xs. We give an approximation of the law of (J0,...,Jn-1) by means of a Euler scheme expansion for the process (Ji). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When Δn = n-1 we deduce from this expansion estimators of the diffusion coefficient of X based on (Ji). These estimators are shown...
Martin Janžura (1988)
Kybernetika
Arfi, Mounir (2008)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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