Teoremas limite para variáveis aleatórias de Bernoulli dependentes

Abstract

In this work, we consider a sequence of correlated Bernoulli variables whose probability of success for the current trial depends conditionally on previous trials. This conditional probability is given as a linear function of the sample mean and has two parameters of which one can assume negative values. We established for this model the strong law of large numbers, an almost sure and L^p convergence, a Gaussian fluctuation of the sum of the random variables with the proposed distribution, an almost sure invariance principle and a weak invariace pinciple, the central limit theorem and the law of the iterated logarithm. Furthermore, we apply all our results to the minimal random walk, a physical model with interesting diffusion characteristics.