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Title: Local asymptotic mixed normality for integrated diffusion processes Authors:  Teppei Ogihara - University of Tokyo (Japan) [presenting]
Abstract: Statistical inference for integrated diffusion processes is studied and asymptotic properties of this model in a high-frequency limit are considered. This model arises when we observe a process after passage through an electric filter, and is also related to the modeling of the stochastic volatility in finance. This model has been previously studied and the local asymptotic mixed normality (LAMN) has been shown when the latent diffusion process is one-dimensional. The LAMN property is important in asymptotic statistical theory and enables us to discuss asymptotic efficiency of estimators. We extend their results of the LAMN property to multi-dimensional diffusion processes which may have a feedback from the integral process. Then, we can apply these results to the Langevin equation which is a model for molecular motion. We also consider the construction of an efficient estimator.