Title: Estimation for degenerate diffusion processes
Authors: Arnaud Gloter - Universite d Evry Val d Essonne (France)
Nakahiro Yoshida - University of Tokyo (Japan) [presenting]
Abstract: A multi-dimensional ergodic diffusion process specified by a system of stochastic differential equations is considered. The first component has a non-degenerate matrix diffusion coefficient and the second component has no diffusion coefficient. Each coefficient has an unknown vector parameter and we estimate these parameters based on long-term high frequency observations. Adaptive and non-adaptive methods are discussed. The convergence rates of the diffusion parameter and the drift parameter in the non-degenerate component are the same as the usual ones but the asymptotic variance is improved. The convergence of the estimator for the parameter in the degenerate component is much faster than others.