A Random Matrix Approximation for the Non-commutative Fractional Brownian Motion |
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| Authors: | Juan Carlos Pardo José-Luis Pérez Victor Pérez-Abreu |
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| Institution: | 1.Department of Probability and Statistics,Centro de Investigación en Matemáticas,Guanajuato,Mexico;2.Department of Probability and Statistics,IIMAS-UNAM,Mexico City,Mexico |
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| 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 (J Theor Probab 27:220–248, 2014). Young and Skorohod stochastic integral techniques and fractional calculus are the main tools used. |
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