LAMN property for hidden processes: the case of integrated diffusions

Details LAMN property for hidden processes: the case of integrated diffusions LAMN property for hidden processes: the case of integrated diffusions

2007-07-02

arxiv.org/abs/0707.0257v1

Annales de l'Institut Henri Poincare (B) Probability and Statistics 44, 1 (2008) 104-128

Mathematics

Probability

Scientific paper

10.1214/07-AIHP111

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process $X$. Our data are given by $ \int_0^1 X_{\frac{s+i}{n}} \dd \mu (s)$ for $i=0,...,n-1$ and the unknown parameter appears in the diffusion coefficient of the process $X$ only. Although the data are nor Markovian neither Gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic expansion. We actually find that the asymptotic information of this model is the same one as for a usual discrete sampling of $X$.

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