On the eigenvalue process of a matrix fractional Brownian motion

DOI10.1016/j.spa.2014.07.017zbMath1301.60051arXiv1401.6584OpenAlexW2073496769MaRDI QIDQ744247

David Nualart, Victor Perez-Abreu

Publication date: 6 October 2014

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.6584

zbMATH Keywords

Young integralDyson processHölder continuous Gaussian processnoncolliding process

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Canonical models for contractions and nonselfadjoint linear operators (47A45)

Related Items (9)

Convergence of the empirical spectral distribution of Gaussian matrix-valued processes ⋮ On the non-commutative fractional Wishart process ⋮ Hitting probabilities of Gaussian random fields and collision of eigenvalues of random matrices ⋮ On the Process of the Eigenvalues of a Hermitian Lévy process ⋮ A random matrix approximation for the non-commutative fractional Brownian motion ⋮ On collision of multiple eigenvalues for matrix-valued Gaussian processes ⋮ Integration with respect to the Hermitian fractional Brownian motion ⋮ Collision of eigenvalues for matrix-valued processes ⋮ Recent advances on eigenvalues of matrix-valued stochastic processes

Cites Work

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• Complex Brownian motion representation of the Dyson model
• Differential equations for Dyson processes
• Global fluctuations in general \(\beta \) Dyson's Brownian motion
• Fractional martingales and characterization of the fractional Brownian motion
• On the traces of Laguerre processes
• Wishart processes
• The Wigner semi-circle law and eigenvalues of matrix-valued diffusions
• Diffusions of perturbed principal component analysis
• Integration with respect to fractal functions and stochastic calculus. I
• Brownian motion in a Weyl chamber, non-colliding particles, and random matrices
• Interacting Brownian particles and the Wigner law
• Diffusing particles with electrostatic repulsion
• Martingale transforms and Girsanov theorem for long-memory Gaussian processes
• Some processes associated with fractional Bessel processes
• Eigenvalues of the Laguerre process as non-colliding squared Bessel processes
• Asymptotic fluctuations of a particle system with singular interaction.
• Stochastic calculus for fractional Brownian motion and related processes.
• The Laguerre process and generalized Hartman-Watson law
• The 1/\(H\)-variation of the divergence integral with respect to the fractional Brownian motion for \(H>1/2\) and fractional Bessel processes
• Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter \(H \in (0,\frac {1}{2})\)
• The variation of the spectrum of a normal matrix
• The Malliavin Calculus and Related Topics
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Stochastic Calculus for Fractional Brownian Motion and Applications

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