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Almost sure versions of limit theorems for random sums of multiindex random variables

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Abstract

In this paper we obtain an almost sure version of a limit theorem for random sums of multiindex random variables that belong to the domain of attraction of a p-stable law.

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References

  1. G. Brosamler, “An Almost Everywhere Central Limit Theorem,” Math. Proc. Cambridge Phil. Soc. 104, 561–574 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Schatte, “On Strong Versions of the Central Limit Theorem,” Math. Nachr. 137, 249–256 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  3. I. Berkes, “On the Almost Sure Central Limit Theorem and Domains of Attraction,” Probab. Theory Related Fields 102, 1–18 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  4. I. A. Ibragimov, “On Almost Everywhere Variants of Limit Theorems,” Phys. Dokl. 350, 301–303 (1996).

    Google Scholar 

  5. I. Berkes and E. Csáki, “A Universal Result in Almost Sure Central Limit Theory,” Stoch. Proc. Appl. 94, 105–134 (2001).

    Article  MATH  Google Scholar 

  6. I. Fazekas and Z. Rychlik, “Almost Sure Central Limit Theorems for Random Fields,” Math. Nachr. 259, 12–18 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. M. Kruglov and G. N. Petrovskaya, “Weak Convergence of Self-Normalized Random Polygonal Lines,” J. ofMath. Sci. 112, 4145–4154 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Rényi, “On the Theory of Order Statistics,” Acts Math. Acad. Sci. Hung. 4, 191–231 (1953).

    Article  MATH  Google Scholar 

  9. V. M. Kruglov and V. Yu. Korolyov, Limit Theorems for Random Sums (Mosk. Univ., Moscow, 1990) [in Russian].

    MATH  Google Scholar 

  10. B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables (GITTL, Moscow-Leningrad, 1949) [in Russian].

    Google Scholar 

  11. P. Billingsley, Convergence of Probability Measures (Wiley, New York-London-Sydney-Toronto, 1968; Nauka, Moscow, 1977).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, 1/37 ul. Professora Nuzhina 1/37, Kazan, 420008, Russia

    A. N. Chuprunov & L. P. Terekhova

Authors
  1. A. N. Chuprunov
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  2. L. P. Terekhova
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Corresponding author

Correspondence to A. N. Chuprunov.

Additional information

Original Russian Text © A.N. Chuprunov and L.P. Terekhova, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 2, pp. 86–96.

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Chuprunov, A.N., Terekhova, L.P. Almost sure versions of limit theorems for random sums of multiindex random variables. Russ Math. 54, 74–83 (2010). https://doi.org/10.3103/S1066369X1002009X

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  • DOI: https://doi.org/10.3103/S1066369X1002009X

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