کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4589523 | 1413357 | 2017 | 24 صفحه PDF | دانلود رایگان |
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.
Journal: Journal of Functional Analysis - Volume 272, Issue 1, 1 January 2017, Pages 339–362