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 () be a diffusion on the interval and a sequence of positive numbers tending to zero. We define as the integral between and of . We give an approximation of the law of by means of a Euler scheme expansion for the process (). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When we deduce from this expansion estimators of the diffusion coefficient of based on (). These estimators are shown to be asymptotically...
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. 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.
LAMN property for hidden processes : the case of integrated diffusions
In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process . Our data are given by d() for =0, …, −1 and the unknown parameter appears in the diffusion coefficient of the process only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood...
Diffusions with measurement errors. II. Optimal estimators
We consider a diffusion process which is observed at times for = 0,1,...,, 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. I. Local Asymptotic Normality
We consider a diffusion process which is observed at times for = 0,1,...,, 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...
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