The functional Breuer-Major theorem

DOI10.1007/s00440-019-00917-1zbMath1434.60108arXiv1808.02378OpenAlexW2887175259WikidataQ127965614 ScholiaQ127965614MaRDI QIDQ2291690

David Nualart, Ivan Nourdin

Publication date: 31 January 2020

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.02378

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Functional limit theorems; invariance principles (60F17)

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High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices, Spectral central limit theorem for additive functionals of isotropic and stationary Gaussian fields, Bounds in \(L^1\) Wasserstein distance on the normal approximation of general M-estimators, Continuous Breuer-Major theorem for vector valued fields, Malliavin-Stein method: a survey of some recent developments, Oscillating Gaussian processes, Approximation of Hilbert-valued gaussians on Dirichlet structures, Cusum tests for changes in the Hurst exponent and volatility of fractional Brownian motion, Rate of convergence in the Breuer-Major theorem via chaos expansions, Multivariate normal approximation on the Wiener space: new bounds in the convex distance, Limit theorems for the realised semicovariances of multivariate Brownian semistationary processes, Functional convergence of sequential \(U\)-processes with size-dependent kernels

Cites Work

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• Convergence of integrated processes of arbitrary Hermite rank
• Introduction to Malliavin Calculus