Abstract
We give novel computationally effective limit theorems for the convergence of the Cesaro-means of certain sequences of random variables. These results are intimately related to various Strong Laws of Large Numbers and, in that way, allow for the extraction of quantitative versions of many of these results. In particular, we produce optimal polynomial bounds in the case of pairwise independent random variables with uniformly bounded variance, improving on known results; furthermore, we obtain a new Baum-Katz type result for this class of random variables. Lastly, we are able to provide a fully quantitative version of a recent result of Chen and Sung that encompasses many limit theorems in the Strong Laws of Large Numbers literature.
| Original language | English |
|---|---|
| Article number | 20 |
| Pages (from-to) | 1-22 |
| Journal | Electronic Journal of Probability |
| Volume | 30 |
| DOIs | |
| Publication status | Acceptance date - 19 Jan 2025 |
Acknowledgements
This article was written as part of the author’s PhD studies under the supervision of Thomas Powell, and I would like to thank him for his support and invaluable guidance. The author would also like to thank Nicholas Pischke for his advice on the presentation and formatting of the results in this article, as well as Cécile Mailler and Nathan Creighton for their helpful comments.Keywords
- large deviations
- Laws of Large Numbers
- limit theorems
- proof mining
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty