Asymptotic theory for fractional regression models via Malliavin calculus

Bourguin, Solesne; Tudor, Ciprian

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Asymptotic theory for fractional regression models via Malliavin calculus

Author(s) :

Bourguin, Solesne [Auteur]
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]
Tudor, Ciprian [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Theoretical Probability

Pages :

536-564

Publisher :

Springer

Publication date :

2010

ISSN :

0894-9840

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

\noindent We study the asymptotic behavior as $n\to \infty$ of the sequence $$S_{n}=\sum_{i=0}^{n-1} K(n^{\alpha} B^{H_{1}}_{i}) \left( B^{H_{2}}_{i+1}-B^{H_{2}}_{i}\right)$$ where $B^{H_{1}}$ and $B^{H_{2}}$ are two ...
Show more >\noindent We study the asymptotic behavior as $n\to \infty$ of the sequence $$S_{n}=\sum_{i=0}^{n-1} K(n^{\alpha} B^{H_{1}}_{i}) \left( B^{H_{2}}_{i+1}-B^{H_{2}}_{i}\right)$$ where $B^{H_{1}}$ and $B^{H_{2}}$ are two independent fractional Brownian motions, $K$ is a kernel function and the bandwidth parameter $\alpha$ satisfies certain hypotheses in terms of $H_{1}$ and $H_{2}$. Its limiting distribution is a mixed normal law involving the local time of the fractional Brownian motion $B^{H_{1}}$. We use the techniques of the Malliavin calculus with respect to the fractional Brownian motion.Show less >

Language :

Anglais

Popular science :

Non

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