General Convergence Rates by the Delayed Sums Method
Abstract
In this study, we propose a delayed sums method to investigate the convergence rates of partial sums. This approach enables general and systematic treatment of the convergence behavior of partial sums, encompassing and extending classical results such as the law of large numbers, the law of logarithm, and the law of the iterated logarithm, as well as convergence with respect to the general norming factors. By establishing almost sure convergence of appropriately defined delayed sums, the proposed method yields explicit convergence rates across a wide range of probabilistic settings. As a result, many convergence problems that were previously treated in isolation can be analyzed within a single coherent theoretical structure.
Fields of Study & Subjects
Probability and Risk Models
Risk and Portfolio Optimization
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- Axioms
- Publisher
- MDPI AG
- Volume
- 15
- Issue
- 2
- Pages
- 92–92
- Publication date
- 26 January 2026
- Language
- EN