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Precise large deviations for widely orthant dependent random variables with different distributions.

Miaomiao Gao1, Kaiyong Wang1, Lamei Chen1

  • 1School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009 P.R. China.

Journal of Inequalities and Applications
|February 2, 2018
PubMed
Summary
This summary is machine-generated.

This study examines precise large deviations for orthant dependent random variables. Researchers establish lower and upper bounds for partial sums under mild conditions, advancing probability theory.

Keywords:
different distributionsdominantly varying tailsprecise large deviationswidely orthant dependent

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Area of Science:

  • Probability Theory
  • Stochastic Processes
  • Mathematical Statistics

Background:

  • Investigates the behavior of partial sums of random variables.
  • Focuses on a specific dependence structure known as widely orthant dependence.
  • Addresses the need for precise large deviation analysis in probability theory.

Purpose of the Study:

  • To investigate precise large deviations for widely orthant dependent random variables.
  • To establish theoretical bounds for the partial sums of these variables.
  • To contribute to the understanding of extreme event probabilities in dependent settings.

Main Methods:

  • Utilizes techniques from large deviation theory.
  • Applies mathematical analysis to derive bounds for partial sums.
  • Considers sequences of random variables with different distributions.

Main Results:

  • Presents precise lower and upper bounds for the large deviations of partial sums.
  • Demonstrates these results under mild conditions for widely orthant dependent random variables.
  • Provides a detailed analysis of the asymptotic behavior of the partial sums.

Conclusions:

  • The findings offer precise characterizations of large deviations for a significant class of dependent random variables.
  • The established bounds are valuable for theoretical applications in probability and statistics.
  • This research enhances the understanding of tail probabilities in complex stochastic systems.