Title: Local asymptotic mixed normality for degenerate diffusion processes
Authors: Teppei Ogihara - University of Tokyo (Japan) [presenting]
Masaaki Fukasawa - Osaka university (Japan)
Abstract: Statistical inference is studied for diffusion processes whose diffusion coefficient is degenerate. Such models arise in the Langevin equation, which represents molecular dynamics and is also related to modeling of the stochastic volatility in finance. We show local asymptotic mixed normality (LAMN) of the statistical models. The LAMN property is important in asymptotic statistical theory and enables us to discuss the asymptotic efficiency of estimators. The LAMN property has been studied for nondegenerate diffusion processes. We extend this result to degenerate diffusion processes by using the scheme with an $L^2$ regularity condition. We also show the LAMN property for partial observations of degenerate diffusion processes. This model is an extension of the LAMN results for one-dimensional integrated diffusion processes to multi-dimensional one.