Diffusions with measurement errors. II. Optimal estimators

Open Access

1 January 2001

journal article
research article
Published by EDP Sciences in ESAIM: Probability and Statistics

Vol. 5, 243-260
https://doi.org/10.1051/ps:2001111

Abstract

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.

Keywords

This publication has 4 references indexed in Scilit:

Diffusions with measurement errors. I. Local Asymptotic Normality
ESAIM: Probability and Statistics, 2001
On continuous conditional Gaussian martingales and stable convergence in law
Published by Springer Nature ,1997
On estimating the diffusion coefficient
Journal of Applied Probability, 1987
Limit Theorems for Stochastic Processes
Published by Springer Nature ,1987