2014/01/25 by David Nualart, Nualart, David, Vı́ctor Pérez-Abreu +2
Economics, Econometrics and Finance · Mathematics · #60H07. Secondary: 47A45 #FOS: Mathematics #Primary: 60H05 #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:47A45 #msc:60H05 #msc:60H07.
paper · pdf · doi:10.48550/arxiv.1401.6584
Title changed and points raised by referees were addressed
openalex publication_date 2014/01/25 · arxiv created 2014/07/27 · arxiv updated 2014/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the process of eigenvalues of a symmetric matrix-valued process which upper diagonal entries are independent one-dimensional Hölder continuous Gaussian processes of order gamma in (1/2,1). Using the stochastic calculus with respect to the Young's integral we show that these eigenvalues do not collide at any time with probability one. When the matrix process has entries that are fractional Brownian motions with Hurst parameter H in (1/2,1), we find a stochastic differential equation in a Malliavin calculus sense for the eigenvalues of the corresponding matrix fractional Brownian motion. A new generalized version of the Itô formula for the multidimensional fractional Brownian motion is first established.