What is it about?
In this paper, we study the almost sure convergence for sequences of asymptotically negative associated (ANA) random variables. As a result, we extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for sequences of independent random variables to sequences of ANA random variables without necessarily adding any extra conditions.
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Why is it important?
The main purpose of this paper is to study the strong limit theorems of partial sums of ANA random variables and try to obtain some new results. We establish Khiatchine– Kolmogorov convergence theorem, the three series theorem and Marcinkiewicz strong law of large numbers for ANA random variables. Our results in this paper extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for independent sequences to ANA sequences without necessarily adding any extra conditions.
Perspectives
The main purpose of this paper is to study the strong limit theorems of partial sums of ANA random variables and try to obtain some new results. We establish Khiatchine– Kolmogorov convergence theorem, the three series theorem and Marcinkiewicz strong law of large numbers for ANA random variables. Our results in this paper extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for independent sequences to ANA sequences without necessarily adding any extra conditions.
Qunying Wu
Guilin University of Technology
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This page is a summary of: SOME LIMITING BEHAVIOR FOR ASYMPTOTICALLY NEGATIVE ASSOCIATED RANDOM VARIABLES, Probability in the Engineering and Informational Sciences, November 2016, Cambridge University Press,
DOI: 10.1017/s0269964816000437.
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