On the eigenvalue process of a matrix fractional Brownian motion

David Nualart and Victor Pérez-Abreu

Stochastic Processes and their Applications, 2014, vol. 124, issue 12, 4266-4282

Abstract: 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 γ∈(1/2,1). Using the stochastic calculus with respect to the Young 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∈(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.

Keywords: Young integral; Noncolliding process; Dyson process; Hölder continuous Gaussian process (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:12:p:4266-4282

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DOI: 10.1016/j.spa.2014.07.017

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