Precise large deviations for sums of random variables with consistently varying tails

Kai Ng, Qihe Tang, Jiaan Yan, Hailiang Yang

Research output: Contribution to journalArticlepeer-review

95 Citations (Scopus)

Abstract

Let {X k , 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 S n and the random sums S N(t), where N(·) is a counting process independent of the sequence {X k , 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.
Original languageEnglish
Pages (from-to)93-107
JournalJournal of Applied Probability
Volume41
Issue number1
DOIs
Publication statusPublished - 2004
Externally publishedYes

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