Research Article Open Access

Complete Convergence of Exchangeable Sequences

George Stoica

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.

Journal of Mathematics and Statistics
Volume 7 No. 2, 2011, 95-97

DOI: https://doi.org/10.3844/jmssp.2011.95.97

Submitted On: 10 March 2006 Published On: 18 May 2011

How to Cite: 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

  • 3,829 Views
  • 2,296 Downloads
  • 0 Citations

Download

Keywords

  • Exchangeable sequences
  • rate of convergence
  • strong law of large numbers