Recent advances on eigenvalues of matrix-valued stochastic processes

DOI10.1016/j.jmva.2021.104847zbMath1480.60056arXiv2109.12262OpenAlexW3205257665MaRDI QIDQ2062789

Yanyan Li

Publication date: 3 January 2022

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.12262

zbMATH Keywords

fractional Brownian motioneigenvalue distributionWishart processDyson Brownian motionBrownian sheetssquared Bessel particle systemmatrix-valued process

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Eigenvalues, singular values, and eigenvectors (15A18) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Cites Work

• On the non-commutative fractional Wishart process
• Central and non-central limit theorems in a free probability setting
• A random matrix approximation for the non-commutative fractional Brownian motion
• Free probability and random matrices
• On strong solutions for positive definite jump diffusions
• Noncolliding squared Bessel processes
• On the eigenvalue process of a matrix fractional Brownian motion
• Estimating the Wishart affine stochastic correlation model using the empirical characteristic function
• Fractional martingales and characterization of the fractional Brownian motion
• On the traces of Laguerre processes
• Spectral analysis of large dimensional random matrices
• Limit laws for random matrices and free products
• Wishart processes
• The Wigner semi-circle law and eigenvalues of matrix-valued diffusions
• Stochastic integrals in the plane
• Diffusions of perturbed principal component analysis
• Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
• Interacting Brownian particles and the Wigner law
• Diffusing particles with electrostatic repulsion
• A survey and some generalizations of Bessel processes
• On squared Bessel particle systems
• Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty}\) kernels
• Eigenvalues of the Laguerre process as non-colliding squared Bessel processes
• Large deviations upper bounds for the laws of matrix-valued processes and non-commutative entropies
• On collision of multiple eigenvalues for matrix-valued Gaussian processes
• High-dimensional central limit theorems for a class of particle systems
• Mean field limit for Coulomb-type flows
• Option pricing when correlations are stochastic: an analytical framework
• Noncolliding Brownian motion and determinantal processes
• Strong solutions of non-colliding particle systems
• Convergence of the empirical spectral distribution of Gaussian matrix-valued processes
• High-dimensional limits of eigenvalue distributions for general Wishart process
• On the law of large numbers for the empirical measure process of generalized Dyson Brownian motion
• An Affine Multicurrency Model with Stochastic Volatility and Stochastic Interest Rates
• Free Random Variables
• The Malliavin Calculus and Related Topics
• Collision of eigenvalues for matrix-valued processes
• Bessel Processes, Schramm–Loewner Evolution, and the Dyson Model
• An Introduction to Random Matrices
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• Multiparameter Processes
• Propagation of Chaos for a Class of First Order Models with Singular Mean Field Interactions
• Brownian Motions of Ellipsoids
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• THE WISHART SHORT RATE MODEL
• Derivative Pricing With Wishart Multivariate Stochastic Volatility
• Multidimensional Yamada-Watanabe theorem and its applications to particle systems
• Continuous Time Wishart Process for Stochastic Risk
• Model-based transductive learning of the kernel matrix
• Fluctations of the empirical law of large random matrices
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