Local Asymptotic Normality Complexity Arising in a Parametric Statistical Lévy Model

Abstract

We consider statistical experiments associated with a Lévy process X=Xtt≥0 observed along a deterministic scheme iun, 1≤i≤n. We assume that under a probability ℙθ, the r.v. Xt, t>0, has a probability density function >o, which is regular enough relative to a parameter θ∈0,∞. We prove that the sequence of the associated statistical models has the LAN property at each θ, and we investigate the case when X is the product of an unknown parameter θ by another Lévy process Y with known characteristics. We illustrate the last results by the case where Y is attracted by a stable process.