Asymptotics for the L^p-deviation of the variance estimator under diffusion

¹ Laboratoire de Statistiques LS-CREST, ENSAE, 3 rue Pierre Larousse, France; doukhan@ensae.fr.
² Universidad Central de Venezuela, Escuela de Matemática, Facultad de Ciencias, AP. 47197, Los Chaguaramos Caracas 1041-A, Venezuela; jleon@euler.ciens.ucv.ve.

Received: 22 October 2002
Revised: 21 October 2003

Abstract

We consider a diffusion process X_t smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the L^p deviations such as