We investigate the process of eigenvalues of a fractional Wishart process defined by N = B*B, where B is the matrix fractional Brownian motion recently studied in 18. Using stochastic calculus with respect to the Young integral we show that, with probability one, the eigenvalues do not collide at any time. When the matrix process B has entries given by independent fractional Brownian motions with Hurst parameter H is an element of (1/2,1), we derive a stochastic differential equation in the Malliavin calculus sense for the eigenvalues of the corresponding fractional Wishart process. Finally, a functional limit theorem for the empirical measure valued process of eigenvalues of a fractional Wishart process is obtained. The limit is characterized and referred to as the non-commutative fractional Wishart process, which constitutes the family of fractional dilations of the free Poisson distribution. (C) 2016 Elsevier Inc. All rights reserved.
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