Asymptotic results for tail probabilities of sums of dependent and heavy-tailed random variables
Tóm tắt
Let X
1,X
2, ... be a sequence of dependent and heavy-tailed random variables with distributions F
1, F
2, ... on (−∞,∞), and let τ be a nonnegative integer-valued random variable independent of the sequence {X
k
, k ≥ 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities
$$S_n = \sum\limits_{k = 1}^n {X_k }$$
and
$$S_{(n)} = \mathop {\max }\limits_{1 \leqslant k \leqslant n} S_k$$
for n > 1, and their randomized versions S
τ
and S
(τ) are studied. Some applications to the risk theory are presented.
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