Complete convergence for partial weighted sums of negatively orthant dependent random variables

Authors

  • Tu Ton That The University of Danang – University of Science and Education, 459 Ton Duc Thang Street, Danang 550000, Vietnam

Keywords:

complete convergence, negatively orthant dependence, weighted sums, limit theorems, dependent random variables

Abstract

Negatively orthant dependence is regarded as a generalisation of independence for random variables, introduced by K. Joag-Dev and F. Proschan. Numerous researchers have investigated inequalities and laws of large numbers for such sequences of random variables. In particular, the concept of complete convergence, defined by P. L. Hsu and H. Robbins, has attracted significant attention. Complete convergence for partial weighted sums of negatively orthant dependent random variables dominated by a random variable X is established. Sufficient conditions for this type of convergence are provided under mild assumptions on the weights and the moments of random variable X.

Author Biography

  • Tu Ton That, The University of Danang – University of Science and Education, 459 Ton Duc Thang Street, Danang 550000, Vietnam

    PhD (physics and mathematics); lecturer at the faculty of mathematics and information technology

References

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Published

2026-01-04

Issue

No. 3 (2025): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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Copyright (c) 2026 Journal of the Belarusian State University. Mathematics and Informatics

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How to Cite

[1]
Ton That, T. 2026. Complete convergence for partial weighted sums of negatively orthant dependent random variables. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Jan. 2026), 38–50.