2015/04/20 by Juan Carlos Pardo, José Luis Pérez, Pardo, Juan Carlos +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Random Matrices and Applications #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1504.05079
openalex publication_date 2015/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the process of eigenvalues of a fractional Wishart process defined as N=B*B, where B is a matrix fractional Brownian motion recently studied by Nualart and Pérez-Abreu. Using stochastic calculus with respect to the Young integral we show that the eigenvalues do not collide at any time with probability one. When the matrix process B has entries given by independent fractional Brownian motions with Hurst parameter H∈(1/2,1) we derive a stochastic differential equation in a 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 free fractional Wishart process which constitutes the family of fractional dilations of the free Poisson distribution.