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Tail Behavior of Sums and Maxima of Sums of Dependent Subexponential Random Variables |
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| Authors: | Yang Yang Kaiyong Wang Remigijus Leipus Jonas ?iaulys |
| Institution: | 1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 210029, P.R. China 2. Department of Mathematics, Southeast University, Nanjing, 210096, P.R. China 3. Department of Information and Computational Science, School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, P.R. China 4. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius, 03225, Lithuania 5. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, Vilnius, 08663, Lithuania |
| Abstract: | In this paper, we consider dependent random variables X k , k=1,2,?? with supports on ?b k ,??), respectively, where the b k ??0 are some finite constants. We derive asymptotic results on the tail probabilities of the quantities $S_{n}=\sum_{k=1}^{n} X_{k}$ , X (n)=max?1??k??n X k and S (n)=max?1??k??n S k , n??1 in the case where the random variables are dependent with heavy-tailed (subexponential) distributions, which substantially generalize the results of Ko and Tang (J. Appl. Probab. 45, 85?C94, 2008). |
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