Abstract
In this paper we study the asymptotic behavior of the tail probabilities of sums of dependent and real-valued random variables whose distributions are assumed to be subexponential and not necessarily of dominated variation. We propose two general dependence assumptions under which the asymptotic behavior of the tail probabilities of the sums is the same as that in the independent case. In particular, the two dependence assumptions are satisfied by multivariate Farlie-Gumbel-Morgenstern distributions.
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Geluk, J., Tang, Q. Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables. J Theor Probab 22, 871–882 (2009). https://doi.org/10.1007/s10959-008-0159-5
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DOI: https://doi.org/10.1007/s10959-008-0159-5
Keywords
- Asymptotic tail probability
- Convolution
- Dominated variation
- Farlie-Gumbel-Morgenstern family
- Subexponentiality