Complete Convergence of Exchangeable Sequences
George Stoica
Journal of Mathematics and Statistics, Volume 7, Issue 2, pp. 95–97 · doi.org/10.3844/jmssp.2011.95.97
Abstract
We prove that exchangeable sequences converge completely in the Baum-Katz sense under the same conditions as i.i.d. sequences do. Problem statement: The research was needed as the rate of convergence in the law of large numbers for exchangeable sequences was previously obtained under restricted hypotheses. Approach: We applied powerful techniques involving inequalities for independent sequences of random variables. Results: We obtained the maximal rate of convergence and provided an example to show that our findings are sharp. Conclusion/Recommendations: The technique used in the paper may be adapted in the similar study for identically distributed sequences.
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Stoica, G. (2011). Complete Convergence of Exchangeable Sequences. Journal of Mathematics and Statistics, 7(2), 95–97. https://doi.org/10.3844/jmssp.2011.95.97
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