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Large deviations in the social systems with threshold conform behavior

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Abstract

The paper considered the distributions of random finite sequences occurring in the theory of collective conformity behavior. A theorem stating that the full principle of large deviations is satisfied for such sequences was formulated and proved. The corresponding action functional was determined.

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References

  1. Huber, P.J. and Elvezio, M.R., Robust Statistics, Hoboken: Wiley, 2009.

    Book  MATH  Google Scholar 

  2. Breer, V.V., Conformal Behavior Models. I, Probl. Upravlen., 2014, no. 1, pp. 2–13.

    Google Scholar 

  3. Breer, V.V., Conformal Behavior Models. II, Probl. Upravlen., 2014, no. 2, pp. 2–17.

    Google Scholar 

  4. Granovetter, M., Threshold Models of Collective Behavior, Am. J. Sociol., 1978, vol. 83, pp. 1420–1443.

    Article  Google Scholar 

  5. Breer, V.V. and Rogatkin, A.D. Probabilistic Model of Threshold Behavior in Multiagent Systems, Autom. Remote Control, 2015, vol. 76, no. 8, pp. 56–77.

    Article  MathSciNet  MATH  Google Scholar 

  6. Deuschel, J. and Stroock, D., Large Deviations, New York: Academic, 1989.

    MATH  Google Scholar 

  7. Puhalskii, A., On Functional Principle of Large Deviations, New Trends Probab. Statist., 1991, vol. 1, pp. 198–218.

    MathSciNet  Google Scholar 

  8. Breer, V.V., Novikov, D.A., and Rogatkin, A.D., Mikro- and Makromodels of Social Networks. I, Probl. Upravlen., 2014, no. 5, pp. 28–33.

    Google Scholar 

  9. Dembo, A. and Zeitouni, O., Large Deviations Techniques and Applications, New York: Springer, 1998.

    Book  MATH  Google Scholar 

  10. Rachev, S., Klebanov, L., Stoyanov, S., et al., The Methods of Distances in the Theory of Probability and Statistics, New York: Springer, 2013.

    Book  MATH  Google Scholar 

  11. Clark, P., Convergence, http://math.uga.edu/˜pete/convergence.pdf.

  12. Billingsley, P., Convergence of Probability Measures, New York: Wiley, 1968. Translated under the title Skhodimost’ veroyatnostnykh mer, Moscow: Nauka, 1977.

    MATH  Google Scholar 

  13. Shiryaev, A.N., Veroyatnost’ (Probability), Moscow: Nauka, 1979.

    MATH  Google Scholar 

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Correspondence to A. D. Rogatkin.

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Original Russian Text © A.D. Rogatkin, 2016, published in Avtomatika i Telemekhanika, 2016, No. 12, pp. 127–135.

This paper was recommended for publication by V.M. Glumov, a member of the Editorial Board

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Rogatkin, A.D. Large deviations in the social systems with threshold conform behavior. Autom Remote Control 77, 2205–2211 (2016). https://doi.org/10.1134/S0005117916120092

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  • DOI: https://doi.org/10.1134/S0005117916120092

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