A Complete Moment Convergence Theorem for Extended Negatively Dependent Random Variables Under Slowly Varying Weights
Abstract
We prove a complete moment convergence criterion for weighted maximal partial sums of extended negatively dependent (END) random variables under slowly varying weights. For every r>1, and for triangular weight arrays that are uniformly bounded, quadratically non-degenerate, and uniformly non-degenerate on their active coefficients, we show that the summability of nr−1l(n)E[(Sn*/n−ε)+] for all ε>0 is equivalent to the weighted moment condition E[|X|r+1l(|X|)]
Fields of Study & Subjects
Probability and Risk Models
Random Matrices and Applications
Financial Risk and Volatility Modeling
Publication details
- Journal / source
- Mathematics
- Publisher
- MDPI AG
- Volume
- 14
- Issue
- 12
- Pages
- 2092–2092
- Publication date
- 11 June 2026
- Language
- EN