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Power laws from randomly sampled continuous-time random walks

Author

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  • Mosetti, Giancarlo
  • Jug, Giancarlo
  • Scalas, Enrico

Abstract

It has been shown by Reed that random-sampling a Wiener process x(t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P(x(T))∼x(T)-β. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Lévy flights (as continuous-time random walks), having Fourier distribution w^(k)=e-|k|α, with the exponent β=α.

Suggested Citation

  • Mosetti, Giancarlo & Jug, Giancarlo & Scalas, Enrico, 2007. "Power laws from randomly sampled continuous-time random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 233-238.
    • Handle: RePEc:eee:phsmap:v:375:y:2007:i:1:p:233-238
    DOI: 10.1016/j.physa.2006.08.065
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    1. anonymous, 1963. "Financing business investment," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Aug, pages 1039-1045.
    2. Gatti, Domenico Delli & Guilmi, Corrado Di & Gaffeo, Edoardo & Giulioni, Gianfranco & Gallegati, Mauro & Palestrini, Antonio, 2005. "A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 489-512, April.
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    Cited by:

    1. Huang, Zhendong & Xiao, Renbin, 2013. "An emergent computation approach to the problem of polygon layout with performance constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5074-5088.

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