Teoremas limite para variáveis aleatórias de Bernoulli dependentes - Rezende, Bruna Luiza de Faria (Universidade Federal de São Carlos, 2023)
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.
Limit theorems for dependent Bernoulli random variables
Keywords: Variáveis aleatórias Bernoulli dependentes; Lei forte dos grandes números; Flutuação Gaussiana; Princípio da invariância fraco e quase certo; Teorema Central do Limite; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::TEOREMAS DE LIMITE; CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::TEORIA GERAL E PROCESSOS ESTOCASTICOS