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Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure

Allez, Romain; Rhodes, Rémi; Vargas, Vincent (2011), Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure. https://basepub.dauphine.fr/handle/123456789/17321

Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-00604400
Date
2011
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
44
Metadata
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Author(s)
Allez, Romain

Rhodes, Rémi

Vargas, Vincent
Abstract (EN)
We study the asymptotics of the spectral distribution for large empirical covariance matrices composed of independent Multifractal Random Walk processes. The asymptotic is taken as the observation lag shrinks to $0$. In this setting, we show that there exists a limiting spectral distribution whose Stieltjes transform is uniquely characterized by equations which we specify.
Subjects / Keywords
Marchenko Pastur; random matrices; MRW; multifractal random walk; empirical covariance matrix; spectral measure

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