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The exactly resolved nonlattice model of random media based on Markov walks with a stable law for jumps

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Abstract

A random-medium model which is a correlated distribution of points (particles) randomly positioned in the 3-dimensional space is considered. The construction of the medium starts from a noncorrelated (Poisson) distribution of parent particles, each of them initiates a finite Markov chain of its descendants. The complete collection of correlation functions of all orders within the scope of the model have been obtained. The use of the 3-dimensional stable law (Lévy law) as a transition probability allows us to present the correlation function in an explicit form.

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Authors and Affiliations

  1. Ulyanovsk Branch of Moscow State University, Lev Tolstoy, 42, 432700, Ulyanovsk, Russia

    V. Uchaikin & G. Gusarov

Authors
  1. V. Uchaikin
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  2. G. Gusarov
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Additional information

Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995, Part II.

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Uchaikin, V., Gusarov, G. The exactly resolved nonlattice model of random media based on Markov walks with a stable law for jumps. J Math Sci 83, 439–446 (1997). https://doi.org/10.1007/BF02400930

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  • DOI: https://doi.org/10.1007/BF02400930

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