Two-sided bounds on the rate of convergence to a stable law

DOI10.1007/BF00534829zbMath0451.60026MaRDI QIDQ3897763

Hall, Peter

Publication date: 1981

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

rate of convergencetwo-sided boundsstable lawdomain of normal attraction

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

Non-integrable stable approximation by Stein's method, On the rate of convergence to a stable limit law. II, A kernel bound for non-symmetric stable distribution and its applications, Some limit theorems for large deviations of sums of independent random variables with common distribution function from the domain of normal attraction of a stable distribution, Approximation of the invariant measure of stable SDEs by an Euler-Maruyama scheme, Approximation of stable law in Wasserstein-1 distance by Stein's method, A bound in the stable ($\alpha $), $1 < \alpha \le 2$, limit theorem for associated random variables with infinite variance, Refining the central limit theorem approximation via extreme value theory, Berry-Esseen bounds and Diophantine approximation, Stein's method for asymmetric \(\alpha \)-stable distributions, with application to the stable CLT, Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model, Rates of convergence of \(\alpha\)-stable random motions, On the rate of convergence of sums of extremes to a stable law, Some remarks on the rate of convergence to stable laws, Simulation of Non-Lipschitz Stochastic Differential Equations Driven by $\alpha$-Stable Noise: A Method Based on Deterministic Homogenization, Approximation to stable law by the Lindeberg principle, Weighted sums of random variables attracted to stable laws

Cites Work

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• [https://portal.mardi4nfdi.de/wiki/Publication:3896292 �ber notwendige und hinreichende Bedingungen f�r Konvergenzgeschwindigkeitsaussagen im Falle einer stabilen Grenzverteilung]
• On the Estimation of the Rate of Convergence in a Limit Theorem with a Stable Limit Law
• On the Accuracy of Approximation in the Central Limit Theorem
• Absolute Estimates of the Rate of Convergence to Stable Laws
• On the influence of moments on the rate of convergence to the normal distribution
• On the Accuracy of Gaussian Approximation to the Distribution Functions of Sums of Independent Variables
• On the Rate of Convergence to a Stable Law
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