The strong law of large numbers for weighted averages under dependence assumptions
Strong laws of large numbers (SLLN) for weighted averages are proved under various dependence assumptions when the variables are not necessarily independent or identically distributed. The results considerably extend the existing results. Weighted versions of the Marcinkiewicz-Zygmund SLLN are also formulated and proved under a similar set up. It seems that such results are not known even for independent and identically distributed random variables.
Key WordsAsymptotically quadrant sub-independence Marcinkiewicz-Zygmund strong laws maximal inequalities mixing conditions mixingale difference strong laws weighted averages
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