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arXiv · 1111.1077

LAN property for some fractional type Brownian motion

Serge Cohen·Fabrice Gamboa·Céline Lacaux·Jean-Michel Loubes
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Abstract

We study asymptotic expansion of the likelihood of a certain class of Gaussian processes characterized by their spectral density $f_\theta$. We consider the case where $f_\theta\PAR{x} \sim_{x\to 0} \ABS{x}^{-\al(\theta)}L_\theta(x)$ with $L_\theta$ a slowly varying function and $\al\PAR{\theta}\in (-\infty,1)$. We prove LAN property for these models which include in particular fractional Brownian motion %$B^\alpha_t,\: \alpha \geq 1/2$ or ARFIMA processes.

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Serge Cohen, Fabrice Gamboa, Céline Lacaux, Jean-Michel Loubes. 2011-11-04. LAN property for some fractional type Brownian motion. https://arxiv.org/abs/1111.1077

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