1. Precise large deviations for sums of random variables with consistently varying tails
- Author
-
Jia-An Yan, Qihe Tang, Kai W. Ng, Hailiang Yang, and Actuarial Science & Mathematical Finance (ASE, FEB)
- Subjects
Statistics and Probability ,Independent and identically distributed random variables ,Discrete mathematics ,Sequence ,Counting process ,General Mathematics ,010102 general mathematics ,Function (mathematics) ,01 natural sciences ,Combinatorics ,Cox process ,010104 statistics & probability ,Heavy-tailed distribution ,Large deviations theory ,0101 mathematics ,Statistics, Probability and Uncertainty ,Random variable ,Mathematics - 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.
- Published
- 2004