Asymptotics for dependent Bernoulli random variables

Lan Wu, Yongcheng Qi, Jingping Yang

Research output: Contribution to journalArticle

10 Scopus citations


This paper considers a sequence of Bernoulli random variables which are dependent in a way that the success probability of a trial conditional on the previous trials depends on the total number of successes achieved prior to the trial. The paper investigates almost sure behaviors for the sequence and proves the strong law of large numbers under weak conditions. For linear probability functions, the paper also obtains the strong law of large numbers, the central limit theorems and the law of the iterated logarithm, extending the results by. James etal. (2008).

Original languageEnglish (US)
Pages (from-to)455-463
Number of pages9
JournalStatistics and Probability Letters
Issue number3
StatePublished - Mar 1 2012


  • Central limit theorem
  • Dependent Bernoulli random variables
  • Law of the iterated logarithm
  • Strong law of large numbers

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