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

Romain Allez (1) , Rémi Rhodes (1) , Vincent Vargas (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Marchenko Pastur; random matrices; MRW; multifractal random walk; empirical covariance matrix; spectral measure

Domaines: Probabilités [math.PR]

Romain Allez, Rémi Rhodes, Vincent Vargas. Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure. 2011. ⟨hal-00604400⟩