Generalization of symmetric α-stable Lévy distributions for q>1

DOI10.1063/1.3305292zbMath1309.60014arXivcond-mat/0606040OpenAlexW1991843946WikidataQ24619344 ScholiaQ24619344MaRDI QIDQ5246615

Murray Gell-Mann, Constantino Tsallis, Sabir R. Umarov, Stanly L. Steinberg

Publication date: 21 April 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0606040

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Taxonomy, cladistics, statistics in mathematical biology (92B10) Fundamental topics (basic mathematics, methodology; applicable to economics in general) (91B02) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31)

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Cites Work

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• On a representation of the inverse \(F_{q}\)-transform
• Is the entropy \(S_q\) extensive or nonextensive?
• On a \(q\) -central limit theorem consistent with nonextensive statistical mechanics
• On Lévy (or stable) distributions and the Williams-Watts model of dielectric relaxation
• Statistical methods in finance
• Generalized algebra within a nonextensive statistics
• Chaos, fractional kinetics, and anomalous transport
• What should a statistical mechanics satisfy to reflect nature?
• Possible generalization of Boltzmann-Gibbs statistics.
• Introduction to Nonextensive Statistical Mechanics
• Nonextensive statistical mechanics and central limit theorems II—Convolution of q-independent random variables
• On multivariate generalizations of the q-central limit theorem consistent with nonextensive statistical mechanics
• Onq-Gaussians and exchangeability
• On 1/ f noise and other distributions with long tails
• On aq-generalization of circular and hyperbolic functions
• Modeling asset returns with alternative stable distributions^*
• Chance and Stability
• A note onq-Gaussians and non-Gaussians in statistical mechanics
• Renormalization group approach to nonextensive statistical mechanics
• Multifractal random walk in copepod behavior
• The random walk's guide to anomalous diffusion: A fractional dynamics approach