Almost sure central limit theorems under minimal conditions

István Berkes, E. Csáki, Lajos Horváth

Research output: Article

21 Citations (Scopus)

Abstract

Let X1, X2, . . . be independent, identically distributed random variables with EX1 = 0, EX21 = 1 and let Sn = ∑k ≤ n Xk. We give nearly optimal criteria for an (unbounded) measurable function f to satisfy the a.s. central limit theorem, i.e., (equation presented) where φ is the standard normal density function.

Original languageEnglish
Pages (from-to)67-76
Number of pages10
JournalStatistics and Probability Letters
Volume37
Issue number1
Publication statusPublished - jan. 15 1998

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Almost Sure Central Limit Theorem
Normal Function
Measurable function
Density Function
Central limit theorem
Identically distributed
Random variable
Standards
Density function
Random variables

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Almost sure central limit theorems under minimal conditions. / Berkes, István; Csáki, E.; Horváth, Lajos.

In: Statistics and Probability Letters, Vol. 37, No. 1, 15.01.1998, p. 67-76.

Research output: Article

Berkes, István ; Csáki, E. ; Horváth, Lajos. / Almost sure central limit theorems under minimal conditions. In: Statistics and Probability Letters. 1998 ; Vol. 37, No. 1. pp. 67-76.
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