On LAN for parametrized continuous periodic signals in a time inhomogeneous diffusion

摘要

We consider a diffusion (ξ_t)t≥0 whose drift involves some T-periodic signal. T is fixed and known, whereas the signal depends on a d-dimensional parameter v∈Θ. Assuming positive Harris recurrence of the grid chain (ξ_(kT))(k∈N_0 and exploiting the periodic structure in the semigroup, we work with path segments and limit theorems for certain functionals (more general than additive functionals) of the process to prove local asymptotic normality (LAN). Then we consider several estimators for the unknown parameter.