Laws of the iterated logarithm for $$\tilde \rho$$ -mixing random variables with normal distribution

Abstract

Consider a \(\tilde \rho\)-mixing sequence of identically distributed random variables with the underlying distribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for \(\tilde \rho\)-mixing sequences of random variables. Our results generalize and improve Theorems 1.2–1.3 of Qi and Cheng (1996) from the i.i.d. case to \(\tilde \rho\)-mixing sequences.