Asymptotic Properties of Extrema of Moving Sums of Independent Non-identically Distributed Variables

In this work, we discuss the asymptotic behavior of minima and maxima of moving sums of independent and non-identically distributed random variables. We first establish some theoretical results associated with the asymptotic behavior of minima and maxima. Then, we apply these results to exponential and normal models. We also derive strong limit results for the minima and maxima of moving sums taken from these two models.