Some limit theorems for dependent Bernoulli random variables

Renato J. Gava and Bruna L.F. Rezende

Statistics & Probability Letters, 2021, vol. 170, issue C

Abstract: We consider a sequence of correlated Bernoulli variables whose probability of success of the current trial depends conditionally on the previous trials as a linear function of the sample mean. We extend the results of Zhang and Zhang (2015) by establishing an almost sure invariance principle and a weak invariance principle in a larger setting. Moreover, we also state a Gaussian fluctuation related to an almost sure and Lp convergence for the model.

Keywords: Dependent Bernoulli random variables; Almost sure invariance principle; Central limit theorem; Law of iterated logarithm; Gaussian fluctuation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2020.109010

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