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

Romain Allez 1, Rémi Rhodes 1, Vincent Vargas 1

(2011-06-28)

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.

1:	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine

Research team: CEREMADE

Subject

:

Mathematics/Probability

Keyword(s): Marchenko Pastur – random matrices – MRW – multifractal random walk – empirical covariance matrix – spectral measure

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From: Rémi Rhodes <>

Submitted on: Tuesday, 28 June 2011 22:50:14

Updated on: Wednesday, 29 June 2011 08:24:34