On the eigenvalue process of a matrix fractional Brownian motion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Nualart, David¹  Perez-Abreu, Victor² 

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[2] Ctr Res Math CIMAT, Dept Probabil & Stat, Guanajuato 36000, Gto, Mexico

关键词: Young integral;    Noncolliding process;    Dyson process;    Holder continuous Gaussian process;   

DOI  :  10.1016/j.spa.2014.07.017

来源: Elsevier

【 摘 要 】

We investigate the process of eigenvalues of a symmetric matrix-valued process which upper diagonal entries are independent one-dimensional Holder continuous Gaussian processes of order gamma is an element of (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 is an element of (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 Ito formula for the multidimensional fractional Brownian motion is first established. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free