Complete Convergence of Exchangeable Sequences

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.