Asymptotics for the tail probability of random sums with a heavy-tailed random number and extended negatively dependent summands

作者：Cheng, Fengyang^*; Li, Na

来源：Chinese Annals of Mathematics Series B, 2014, 35(1): 69-78.

DOI：10.1007/s11401-013-0815-7

• Asymptotic behavior
• Random sums
• Heavy-Tailed distribution

Let {X,X (k) : k >= 1} be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX > 0. Let tau be a nonnegative integer-valued random variable, independent of {X,X (k) : k >= 1}. In this paper, the authors obtain the necessary and sufficient conditions for the random sums S-tau = (n=1)Sigma(tau) X-n to have a consistently varying tail when the random number tau has a heavier tail than the summands, i.e.,
P(X > x)/P(tau > x) -> 0

• 出版日期2014-1
• 单位中国石油大学（华东）; 苏州大学