Convergence of the spectrum of empirical covariance matrices for independent MRW processes

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.ouinonouirechercheInternationa