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Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables

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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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Authors and Affiliations

  1. Department of Mathematics, The Petroleum Institute, P.O. Box 2533, Abu Dhabi, United Arab Emirates

    Jaap Geluk

  2. Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA, 52242, USA

    Qihe Tang

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  1. Jaap Geluk
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  2. Qihe Tang
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Correspondence to Qihe Tang.

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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

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