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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Heavy-tailed Distributions in Some Stochastic Dynamical Models

Discontinuity, Nonlinearity and Complexity 1(1) 2012 1–40 | DOI:10.5890/DNC.2012.02.001

Ph. Blanchard, T. Kruger, D. Volchenkov$^1$

$^1$ Center of Excellence Cognitive Interaction Technology, Universit¨at Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany

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Abstract

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed some models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the Degree-Mass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavy-tailed distributions appear in them as the emergent phenomena sensitive for coupling rules essential for the entire dynamics.

Acknowledgments

We would like to thank Bruno Cessac, Elena Floriani, Max Hongler, and Ricardo Lima for numerous discussions.

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