Journal of Applied Probability

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

Kai W. Ng, Qihe Tang, Jia-An Yan, and Hailiang Yang

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Abstract

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 F̅(x) = 1 - F(x) 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.

Article information

Source
J. Appl. Probab. Volume 41, Number 1 (2004), 93-107.

Dates
First available in Project Euclid: 18 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.jap/1077134670

Digital Object Identifier
doi:10.1239/jap/1077134670

Mathematical Reviews number (MathSciNet)
MR2036274

Zentralblatt MATH identifier
1051.60032

Subjects
Primary: 60F10: Large deviations 60F05: Central limit and other weak theorems 60G50: Sums of independent random variables; random walks

Keywords
Consistently varying tail doubly stochastic process heavy tail Matuszewska index negative association precise large deviations random sums

Citation

Ng, Kai W.; Tang, Qihe; Yan, Jia-An; Yang, Hailiang. Precise large deviations for sums of random variables with consistently varying tails. J. Appl. Probab. 41 (2004), no. 1, 93--107. doi:10.1239/jap/1077134670. http://projecteuclid.org/euclid.jap/1077134670.


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