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We consider a diffusion $(\xi_t)_{t\ge 0}$ with some $T$-periodic timedependent input term contained in the drift: under an unknown parameter$\vth\in\Theta$, some discontinuity - an additional periodic signal - occurs attimes $kT{+}\vth$, $k\in\bbn$. Assuming positive Harris recurrence of$(\xi_{kT})_{k\in\bbn_0}$ and exploiting the periodicity structure, we provelimit theorems for certain martingales and functionals of the process$(\xi_t)_{t\ge 0}$. They allow to consider the statistical model parametrizedby $\vth\in\Theta$ locally in small neighbourhoods of some fixed $\vth$, withradius $1/n$ as $\nto$. We prove convergence of local models to a limitexperiment studied by Ibragimov and Khasminskii [IH 81] and discuss thebehaviour of estimators under contiguous alternatives.

Estimating discontinuous periodic signals in a non-time homogeneous diffusion process