On Sevast'yanov's theorem

M. Denker, N. Kan

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Abstract

In this paper we prove Poisson limit theorems for occupancy vectors Sn = X1 n + ⋯ + Xnn (n ≥ 1), where { Xln : l = 1, ..., n } form some dependent k-dimensional random vectors with values in the set of linearly independent vectors e1, ..., ek ∈ Rk. Our method extends the result of Sevast'yanov in [Sevast'yanov, B. A., 1972. Poisson limit law for a scheme of sums of dependent random variables. Theory Probab. Appl. 17, 695-699] for the case k = 2.

Original languageEnglish (US)
Pages (from-to)272-279
Number of pages8
JournalStatistics and Probability Letters
Volume77
Issue number3
DOIs
Publication statusPublished - Feb 1 2007

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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