# LAN property for some fractional type Brownian motion

2 BIGS - Biology, genetics and statistics
IECN - Institut Élie Cartan de Nancy, INRIA Lorraine
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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Journal articles
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Cited literature [23 references]

https://hal.archives-ouvertes.fr/hal-00638121
Contributor : Jean-Michel Loubes <>
Submitted on : Thursday, November 3, 2011 - 11:51:10 PM
Last modification on : Thursday, February 11, 2021 - 2:48:32 PM
Long-term archiving on: : Thursday, November 15, 2012 - 11:05:50 AM

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LAN_Final_2011.pdf
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### Identifiers

• HAL Id : hal-00638121, version 1
• ARXIV : 1111.1077

### Citation

Serge Cohen, Fabrice Gamboa, Céline Lacaux, Jean-Michel Loubes. LAN property for some fractional type Brownian motion. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2013, 10 (1), pp.91-106. ⟨hal-00638121⟩

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