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[Maximal inequalities play a crucial role in many probabilistic limit theorem; for instance, the law of large numbers, the law of the iterated logarithm, the martingale limit theorem and the central limit theorem. Let X1, X2, … be random variables with partial sums Sk = X1 + ⋯ + Xk. Then a maximal inequality gives conditions ensuring that the maximal partial sum Mn = max1 ≤ i ≤ n Si is of the same order as the last sum Sn. In the literature there exist large number of maximal inequalities if X1, X2, … are independent but much fewer for dependent random variables. In this paper, I shall focus on random variables X1, X2, … having some weak dependence properties; such as positive and negative In-correlation, mixing conditions and weak martingale conditions.]
Published: Sep 22, 2016
Keywords: Demi-martingales; Integral orderings; Mixing conditions; Negative and positive correlation
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