A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion

2014/09/30 by Juan Carlos Pardo, Pardo, Juan Carlos, Victor Pérez-Abreu +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1409.8532

arxiv created 2015/06/21 · arxiv updated 2015/06/23

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.

Related

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• On the Free Fractional Wishart Process
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• Fractional Brownian motion and the Markov Property
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