Abstract
Let be either a sequence of arbitrary random variables, or a martingale difference sequence, or a centred sequence with a suitable level of negative dependence. We prove Baum–Katz type theorems by only assuming that the variables
satisfy a uniform moment bound condition. We also prove that this condition is best possible even for sequences of centred, independent random variables. This leads to Marcinkiewicz–Zygmund type strong laws of large numbers with estimate for the rate of convergence.
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Notes
No potential conflict of interest was reported by the authors.