Article ID Journal Published Year Pages File Type
4589523 Journal of Functional Analysis 2017 24 Pages PDF
Abstract

We investigate the process of eigenvalues of a fractional Wishart process defined by N=B⁎BN=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∈(1/2,1)H∈(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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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