Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Random allocation for a class of polya plans

  • 13 Accesses

  • 2 Citations


We consider N + 1-dimensional Polya random walks with stopping limit described by a symmetric function of N coordinates. For such plans we obtain the asymptotic distribution of the number of exits realized r times.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    Ya. P. Lumel'skii, “Random walks corresponding to generalized urn schemes,” Dokl. Akad. Nauk SSSR,209, No. 6 (1973).

  2. 2.

    Ya. M. L'vovskii, “Random allocation of particles to cells corresponding to a Polya distribution,” Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Perm' Univ. (1986).

  3. 3.

    V. A. Ivanov, G. I. Ivchenko, and Yu. I. Medvedev, Discrete Problems of Probability Theory, Itogi Nauki i Tekhniki, Teor. Veroyatn. Mat. Statistika. Teor. Kibern.,22 (1984).

  4. 4.

    V. F. Kolchin, B. A. Sevast'yanov, and V. P. Chistyakov, Random Allocations [in Russian], Moscow (1976).

  5. 5.

    V. F. Kolchin, Random Mappings [in Russian], Moscow (1984).

  6. 6.

    W. Feller, Introduction to Probability Theory and Its Applications [Russian translation], Vol. 1, Moscow (1984).

  7. 7.

    T. V. Ivanova, “Limit theorems in a scheme of successive filling of cells for a partition of them into groups,” Nauchn. Tr. Kuban. Univ. No. 247 (1977).

  8. 8.

    Ya. M. L'vovskii and E. G. Tsylova, “New asymptotic formulas for a multidimensional Polya distribution,” Dep. in VINITI, 1985, No. 7793-C.

  9. 9.

    E. G. Tsylova, “α-Generalized Poisson distribution,” Dep. in VINITI, 1985. No. 7794-C.

  10. 10.

    Wen Chen Chen, “Some local limit theorems in the symmetric Direchlet multinomials urn models,” Ann. Inst. Statist. Math.,33, No. 3 (1981).

  11. 11.

    Ya. P. Lumel'skii and Ya. M. L'vovskii, “Asymptotic expansions of some multidimensional discrete distributions,” Dep. in VINITI. 1979. No. 3155.

Download references

Author information

Additional information

Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 130–143, 1988.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

L'vovskii, Y.M. Random allocation for a class of polya plans. J Math Sci 56, 2481–2488 (1991). https://doi.org/10.1007/BF01096118

Download citation


  • Symmetric Function
  • Asymptotic Distribution
  • Random Allocation
  • Polya Plan