Deviation inequalities and moderate deviations for estimators of parameters in an Ornstein-Uhlenbeck process with linear drift.
Die Schätzung des linearen Todesprozesses bei fehlerbehafteten Beobachtungen.
Diffusions with measurement errors. I. Local asymptotic normality
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...
Diffusions with measurement errors. I. Local Asymptotic Normality
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....
Diffusions with measurement errors. II. Optimal estimators
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.
Diffusions with measurement errors. II. Optimal estimators
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.
Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient
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...
Divergences of Gauss-Markov random fields with application to statistical inference
Drift estimation from -mixing sequences.