Central and non-central limit theorems in a free probability setting

DOI10.1007/s10959-012-0443-2zbMath1314.46077arXiv1110.2703OpenAlexW2149294920MaRDI QIDQ457102

Ivan Nourdin, Murad S. Taqqu

Publication date: 26 September 2014

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2703

zbMATH Keywords

fractional Brownian motionfree Brownian motionconvergence in distributioncentral limit theoremRosenblatt processnon-central limit theoremfree probabilityWigner integral

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Free probability and free operator algebras (46L54) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (10)

On the non-commutative fractional Wishart process ⋮ Limit theorems for filtered long-range dependent random fields ⋮ Integration with respect to the non-commutative fractional Brownian motion ⋮ Selfsimilar free additive processes and freely selfdecomposable distributions ⋮ On eigenvalues of the Brownian sheet matrix ⋮ A random matrix approximation for the non-commutative fractional Brownian motion ⋮ Integration with respect to the Hermitian fractional Brownian motion ⋮ Recent advances on eigenvalues of matrix-valued stochastic processes ⋮ Asymptotic behavior of large Gaussian correlated Wishart matrices ⋮ On the non-commutative multifractional Brownian motion

Cites Work

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• Wigner chaos and the fourth moment
• On the distribution of the roots of certain symmetric matrices
• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• Central limit theorems for non-linear functionals of Gaussian fields
• Limit laws for random matrices and free products
• Stochastic calculus with respect to free Brownian motion and analysis on Wigner space
• Normal Approximations with Malliavin Calculus
• Lectures on the Combinatorics of Free Probability
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
• Appell polynomials and their relatives
• Fractional Brownian Motions, Fractional Noises and Applications

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