A complete characterization of a correlated Bernoulli process
We present a complete characterization of the asymptotic behaviour of a correlated Bernoulli sequence { which depends on the parameter $θ\in [0,1]$. A martingale theory based approach will allow} us to prove versions of the law of large numbers, quadratic strong law, law of iterated logarithm, almost sure central limit theorem and functional central limit theorem, in the case $θ\le 1/2$. For $θ> 1/2$, we will obtain a strong convergence to a non-degenerated random variable, including a central limit theorem and a law of iterated logarithm for the fluctuations.
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