Limit laws for norms of IID samples with Weibull tails

DOI10.1007/s10959-006-0036-zzbMath1128.60016OpenAlexW2035032507MaRDI QIDQ867094

Leonid V. Bogachev

Publication date: 14 February 2007

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

Full work available at URL: https://doi.org/10.1007/s10959-006-0036-z

zbMATH Keywords

stable lawscentral limit theoremsums of independent random variablesweak limit theoremsinfinite divisible laws

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items

Limit laws for power sums and norms of i.i.d. samples, Convergence and relative compactness in distribution of sequences of random hypermeasures, Consistency of \(p\)-norm based tests in high dimensions: characterization, monotonicity, domination, Functional limit theorems for sums of independent geometric Lévy processes, Limit Theorems for Random Exponentials: The Bounded Support Case, Complex random energy model: zeros and fluctuations, Limit laws for the norms of extremal samples, Laplacian with respect to a measure on a Hilbert space and an \(L_2\)-version of the Dirichlet problem for the Poisson equation, Stable limit laws for the parabolic Anderson model between quenched and annealed behaviour

Cites Work

• Tauberian theorems of exponential type
• Limit distributions of norms of vectors of positive i. i. d. random variables
• Limit theorems for sums of random exponentials
• Inequalities for the $r$th Absolute Moment of a Sum of Random Variables, $1 \leqq r \leqq 2$
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