Fisher information and convergence to stable laws

DOI10.3150/13-BEJ535zbMath1315.60031arXiv1205.3637MaRDI QIDQ396022

Gennadiy P. Chistyakov, Friedrich Götze, Sergey G. Bobkov

Publication date: 8 August 2014

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.3637

zbMATH Keywords

stable lawsFisher informationcentral limit theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Measures of information, entropy (94A17)

Related Items (5)

The fractional Fisher information and the central limit theorem for stable laws ⋮ Score functions, generalized relative Fisher information and applications ⋮ Poincaré-type inequalities for stable densities ⋮ Entropy inequalities for stable densities and strengthened central limit theorems ⋮ Convergence and asymptotic approximations to universal distributions in probability

Cites Work

• Convergence to stable laws in relative entropy
• Bounds for characteristic functions in terms of quantiles and entropy
• Entropy and the central limit theorem
• Unimodality of infinitely divisible distribution functions of class L
• Fisher information inequalities and the central limit theorem
• Some inequalities satisfied by the quantities of information of Fisher and Shannon
• An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions
• Regularly varying functions
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