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 anunknown $d$-dimensional parameter $\vartheta\in\Theta$. Assuming positiveHarris recurrence of the grid chain $(\xi_{kT})_{k\in\mathbb{N}_0}$ andexploiting the periodic structure of the semigroup, we work with path segmentsand limit theorems for certain functionals (more general than additivefunctionals) of the process to prove local asymptotic normality (LAN). Then weconsider several estimators for the unknown parameter.
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机译：我们考虑扩散$（\ xi_t）_ {t \ ge 0} $，其漂移涉及$ T $周期信号。 $ T $是固定且已知的，而信号取决于未知的$ d $维参数$ \ vartheta \ in \ Theta $。假设网格链$（\ xi_ {kT}）_ {k \ in \ mathbb {N} _0} $的正Harris递归并利用半群的周期结构，我们使用路径段并限制某些函数的定理（比证明局部渐近正态性（LAN）的过程。然后，我们考虑未知参数的多个估计量。
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