On the convergence of series of moments for row sums of random variables

2019/01/18 by João Lita da Silva, da Silva, João Lita
Computer Science · Decision Sciences · Mathematics · #60F15 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1901.06147

openalex publication_date 2019/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Given a triangular array \X_n,k, 1 \leqslant k \leqslant n, n \geqslant 1 \ of random variables satisfying 𝔼 | X_n,k |^p < ∞ for some p \geqslant 1 and sequences \b_n \, \c_n \ of positive real numbers, we shall prove that ∑_n=1^∞ c_n 𝔼 [ |∑_k=1ⁿ (X_n,k - 𝔼 X_n,k)| / b_n - ε ]₊^p < ∞, where x₊ = max(x,0). Our results are announced in a general setting, allowing us to obtain the convergence of the series in question under various types of dependence.

Related

• Convergence of series of moments on general exponential inequality
• On the rates of convergence for sums of dependent random variables
• Strong laws of large numbers for arrays of row-wise extended negatively dependent random variables
• On the convergence of series of dependent random variables
• Complete moment and integral convergence for sums of negatively associated random variables