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arXiv · 1606.02794

Baum-Katz type theorems with exact threshold

Richárd Balka·Tibor Tómács
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Abstract

Let $\{X_n\}_{n\geq 1}$ be either a sequence of arbitrary random variables, or a martingale difference sequence, or a centered sequence with a suitable level of negative dependence. We prove Baum-Katz type theorems by only assuming that the variables $X_n$ satisfy a uniform moment bound condition. We also prove that this condition is best possible even for sequences of centered, 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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Richárd Balka, Tibor Tómács. 2016-06-09. Baum-Katz type theorems with exact threshold. https://arxiv.org/abs/1606.02794

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