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A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion (1409.8532v2)
Published 30 Sep 2014 in math.PR
Abstract: A functional limit theorem for the empirical measure-valued process of eigenvalues of a matrix fractional Brownian motion is obtained. It is shown that the limiting measure-valued process is the non-commutative fractional Brownian motion recently introduced by Nourdin and Taqqu. Young and Skorohod stochastic integral techniques and fractional calculus are the main tools used.