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Asymptotics of random sums of negatively dependent random variables in the presence of dominatedly varying tails |
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| Authors: | Yang Yang Remigijus Leipus Jonas ?iaulys |
| Affiliation: | 1. Department of Mathematics, Southeast University, Nanjing, 210096, PR China 2. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 210029, PR China 3. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania 4. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania |
| Abstract: | Let X 1 , X 2 , . . . be a sequence of negatively dependent and identically distributed random variables, and let N be a counting random variable independent of X i ’s. In this paper, we study the asymptotics for the tail probability of the random sum SN = ?k = 1N Xk {S_N} = sumnolimits_{k = 1}^N {{X_k}} in the presence of heavy tails. We consider the following three cases: (i) P(N > x) = o(P(X 1 > x)), and the distribution function (d.f.) of X 1 is dominatedly varying; (ii) P(X 1 > x) = o(P(N > x)), and the d.f. of N is dominatedly varying; (iii) the tails of X 1 and N are asymptotically comparable and dominatedly varying. |
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