Uniform convexity and the distribution of the norm for a Gaussian measure

DOI10.1007/BF00366272zbMath0554.60007MaRDI QIDQ760085

Michel Talagrand, WanSoo T. Rhee

Publication date: 1986

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

zbMATH Keywords

modulus of uniform convexitydistribution of the norm

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Continuity and singularity of induced measures (60G30)

Related Items (13)

On Gaussian approximation of Hilbert space valued discrete time martingales ⋮ On distribution of the norm for normal random elements in the space of continuous functions ⋮ Recursive estimation: asymptotic confidence regions by empirical quantiles ⋮ Gaussian measures on linear spaces ⋮ Smoothness of the distribution of the norm in uniformly convex Banach spaces ⋮ The measure of a translated ball in uniformly convex spaces ⋮ Nonuniform estimates in the central limit theorem in Banach spaces ⋮ On the distribution of the norm for a multidimensional Brownian bridge ⋮ Theorems of large deviations in the multivariate invariance principle ⋮ Extremes and crossings for differentiable stationary processes with application to Gaussian processes in \(\mathbb{R}{}^ m\) and Hilbert space ⋮ Densities of distributions of homogeneous functions of Gaussian random vectors ⋮ Distribution of the norm of a multidimensional Wiener process ⋮ Asymptotic expansions in the integral and local limit theorems in Banach spaces with applications to \(\omega\)-statistics

Cites Work

• Unnamed Item
• On the rate of convergence in the central limit theorem in Banach spaces
• Uniform bound in the central limit theorem for Banach space valued dependent random variables
• Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm
• Martingales with values in uniformly convex spaces
• Symétrisation dans l'espace de Gauss.
• On the Rate of Convergence in the Central Limit Theorem in Certain Banach Spaces
• Bad rates of convergence for the central limit theorem in Hilbert space

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