Precise large deviations for sums of random variables with consistently varying tails
2004 ◽
Vol 41
(1)
◽
pp. 93-107
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Keyword(s):
Let {Xk, k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums Sn and the random sums SN(t), where N(·) is a counting process independent of the sequence {Xk, k ≥ 1}. The obtained results improve some related classical ones. Applications to a risk model with negatively associated claim occurrences and to a risk model with a doubly stochastic arrival process (extended Cox process) are proposed.
2004 ◽
Vol 41
(01)
◽
pp. 93-107
◽
2013 ◽
Vol 42
(24)
◽
pp. 4444-4459
◽
2007 ◽
Vol 44
(04)
◽
pp. 889-900
◽
2007 ◽
Vol 44
(4)
◽
pp. 889-900
◽
2013 ◽
Vol 43
(4)
◽
pp. 1395-1414
◽
2010 ◽
Vol 80
(19-20)
◽
pp. 1559-1567
◽
2021 ◽
Vol 37
(3)
◽
pp. 539-547
Keyword(s):