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arXiv · 1610.04093

Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous Diffusion

Simon Holbach
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Abstract

We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $θ$. We prove Local Asymptotic Normality (LAN) jointly in $θ$ and $T$ for the statistical experiment arising from continuous observation of this diffusion. The local scale turns out to be $n^{-1/2}$ for the shape parameter and $n^{-3/2}$ for the periodicity which generalizes known results about LAN when either $θ$ or $T$ is assumed to be known.

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Simon Holbach. 2017-01-16. Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous Diffusion. https://doi.org/10.1007/s11203-017-9157-5

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