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

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

2010-03-18

arxiv.org/abs/1003.3546v1

Mathematics

Statistics Theory

Scientific paper

We consider a diffusion $(\xi_t)_{t\ge 0}$ whose drift involves a $T$-periodic signal. $T$ is fixed and known, whereas the signal depends on an unknown $d$-dimensional parameter $\vartheta\in\Theta$. Assuming positive Harris recurrence of the grid chain $(\xi_{kT})_{k\in\mathbb{N}_0}$ and exploiting the periodic structure of 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.

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