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General model of subtraction of stochastic variables. Attractor and stability analysis

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  • Beltrán del Río, M.
  • Cocho, G.
  • Mansilla, R.

Abstract

We introduce a general process designed to model stochastic systems in which the dependence of random variables is not through addition only but combined addition and subtraction with bounded ranges, and whose probabilistic factors have compact support. We show that, still retaining much of the general essence of the Central Limit Theorem, this process presents a functional attractor which is neither Gaussian nor Lévy like, and is precisely akin numerically to a probability density function shown in previous works to have ubiquitous character, namely the two-parameter beta distribution.

Suggested Citation

  • Beltrán del Río, M. & Cocho, G. & Mansilla, R., 2011. "General model of subtraction of stochastic variables. Attractor and stability analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 154-160.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:2:p:154-160
    DOI: 10.1016/j.physa.2010.09.035
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    References listed on IDEAS

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    1. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
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    Cited by:

    1. Alvarez-Martínez, R. & Cocho, G. & Rodríguez, R.F. & Martínez-Mekler, G., 2014. "Birth and death master equation for the evolution of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 198-208.
    2. Li, Wentian, 2012. "Fitting Chinese syllable-to-character mapping spectrum by the beta rank function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1515-1518.

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    Keywords

    Central Limit Theorem; Random systems;

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