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Consider a scalar reflected diffusion $(X_t:t\geq 0)$, where the unknowndrift function $b$ is modelled nonparametrically. We show that in the lowfrequency sampling case, when the sample consists of$(X_0,X_\Delta,...,X_{n\Delta})$ for some fixed sampling distance $\Delta>0$,the model satisfies the local asymptotic normality (LAN) property, assumingthat $b$ satisfies some mild regularity assumptions. This is established byusing the connections of diffusion processes to elliptic and parabolic PDEs.The key tools will be regularity estimates from the theory of parabolic PDEs aswell as a detailed analysis of the spectral properties of the ellipticdifferential operator related to $(X_t:t\geq 0)$.

The nonparametric LAN expansion for discretely observed diffusions