Ukrainian Mathematical Journal

, Volume 49, Issue 11, pp 1768–1776 | Cite as

On one stochastic model that leads to a stable distribution

  • E. S. Sinaiskii
Brief Communications


We consider an integral equation describing the contagion phenomenon, in particular, the equation of the state of a hereditarily elastic body, and interpret this equation as a stochastic model in which the Rabotnov exponent of fractional order plays the role of density of probability of random delay time. We invesgigate the approximation of the distribution for sums of values with a given density to the stable distribution law and establish the principal characteristics of the corresponding renewal process.


Stochastic Model Fractional Order Elastic Body Renewal Process Laplace Transformation 
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© Plenum Publishing Corporation 1998

Authors and Affiliations

  • E. S. Sinaiskii

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