# On Sevast'yanov's theorem

M. Denker, N. Kan

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 language English (US) 272-279 8 Statistics and Probability Letters 77 3 https://doi.org/10.1016/j.spl.2006.07.008 Published - Feb 1 2007

### Fingerprint

Siméon Denis Poisson
Limit Laws
Dependent Random Variables
Random Vector
Limit Theorems
Theorem
Linearly
Dependent
Limit theorems
Random variables

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty

### Cite this

Denker, M. ; Kan, N. / On Sevast'yanov's theorem. In: Statistics and Probability Letters. 2007 ; Vol. 77, No. 3. pp. 272-279.
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On Sevast'yanov's theorem. / Denker, M.; Kan, N.

In: Statistics and Probability Letters, Vol. 77, No. 3, 01.02.2007, p. 272-279.

Research output: Contribution to journalArticle

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AU - Kan, N.

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