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Asymptotics for the Lp -deviation of the variance estimator under diffusion
Published online by Cambridge University Press: 15 September 2004
Abstract
We consider a diffusion process X t smoothed with (small)sampling parameter ε. As in Berzin, León and Ortega(2001), we consider a kernel estimate $\widehat{\alpha}_{\varepsilon}$ 
with window h(ε) of afunction α of its variance. In order to exhibit globaltests of hypothesis, we derive here central limit theorems forthe Lp deviations such as \[ \frac1{\sqrt{h}}\left(\frac{h}\varepsilon\right)^{\frac{p}2}\left(\left\|\widehat{\alpha}_{\varepsilon}-{\alpha}\right\|_p^p-\mbox{I E}\left\|\widehat{\alpha}_{\varepsilon}-{\alpha}\right\|_p^p\right).\] 
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- © EDP Sciences, SMAI, 2004
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