Sufficient conditions for asymptotic normality of sums of values of discrete random fields, dependent in strips

  • L. A. Zolotukhina
  • V. N. Chugueva


Sufficient conditions are given for the asymptotic normality of a sum of values of a field on a square of the integer lattice in R2 with the side n → ∞ for normalization by the quantity (2n+1)3/2. Moreover, the values of the field are dependent on strips of fixed width. The method of moments is used for proof.


Random Field Asymptotic Normality Integer Lattice Fixed Width Discrete Random Field 
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Literature cited

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    L. A. Zolotukhina and V. N. Chugueva, “The central limit theorem for a class of random vector fields,” Mat. Zametki,14, No. 4, 549–558 (1973).Google Scholar
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    M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, Vol. 1: Distribution Theory, Chames Griffins, London (1963).Google Scholar
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    L. A. Zolotukhina, K. P. Latyshev, and V. N. Chugueva, “Stochastic models of lamellar media and stochastic properties of reflected waves propagating in these media,” Tr. Mat. Inst. Akad. Nauk SSSR,95, 42–97 (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • L. A. Zolotukhina
    • 1
  • V. N. Chugueva
    • 1
  1. 1.Leningrad Section of the V. A. Steklov Mathematics InstituteAcademy of Sciences of the USSRUSSR

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