Randomly sampled Riemann sums and complete convergence in the law of large numbers for a case without identical distribution

DOI10.1090/S0002-9939-96-03100-0zbMath0843.60031OpenAlexW1747004765MaRDI QIDQ4875541

Alexander R. Pruss

Publication date: 13 August 1996

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-96-03100-0

zbMATH Keywords

complete convergencelaw of large numberscentral limit theoremLebesgue integralRiemann sumsrate of convergence in the central limit theoremrate of convergence in the law of large numbers

Mathematics Subject Classification ID

Strong limit theorems (60F15) Large deviations (60F10) Integrals of Riemann, Stieltjes and Lebesgue type (26A42)

Related Items (13)

Convergence rates for the law of large numbers for arrays ⋮ A general Hsu-Robbins-Erdős type estimate of tail probabilities of sums of independent identically distributed random variables ⋮ Remarks on summability of series formed of deviation probabilities of sums of independent identically distributed random variables ⋮ A random approach to the Lebesgue integral ⋮ A comparison inequality for sums of independent random variables ⋮ On complete convergence in Marcinkiewicz-Zygmund type SLLN for negatively associated random variables ⋮ Convergence rates in the SLLN for some classes of dependent random fields ⋮ Further randomization of Riemann sums leading to the Lebesgue integral ⋮ An approach to complete convergence theorems for dependent random fields via application of Fuk-Nagaev inequality ⋮ Random Riemann sum estimator versus Monte Carlo ⋮ On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables ⋮ On Some Conditions for Complete Convergence for Arrays of Rowwise Negatively Dependent Random Variables ⋮ On the rate of convergence in the strong law of large numbers for martingales

Cites Work

• The Lebesgue Integral as the Almost Sure Limit of Random Riemann Sums
• Convergence Rates in the Law of Large Numbers
• Complete Convergence and the Law of Large Numbers
• On a Theorem of Hsu and Robbins
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Randomly sampled Riemann sums and complete convergence in the law of large numbers for a case without identical distribution