Chen, Yu; Zhang, Weiping Large deviations for random sums of negatively dependent random variables with consistently varying tails. (English) Zbl 1117.60025 Stat. Probab. Lett. 77, No. 5, 530-538 (2007). Summary: Let \(\{X_k\), \(k=1,2,\dots\}\) be a sequence of negatively dependent random variables with common distribution \(F\) and finite expectation \(\mu\). Under the assumption that the tail probability \(\overline F(z)=1-F(x)\) is consistently varying as \(x\) tends to infinity, this paper investigates precise large deviations for the random sum \(S_{N(t)}=\sum^{N(t)}_{n=1}X_n\), where \(\{N(t)\), \(t\geq 0\}\) is a nonnegative and integer-valued process independent of \(\{X_k\), \(k=1,2,\dots\}\). Cited in 2 ReviewsCited in 23 Documents MSC: 60F10 Large deviations Keywords:negative dependence; large deviation; random sum; consistently varying tail PDFBibTeX XMLCite \textit{Y. Chen} and \textit{W. Zhang}, Stat. Probab. Lett. 77, No. 5, 530--538 (2007; Zbl 1117.60025) Full Text: DOI References: [1] Alam, K.; Saxena, K. M.L., Positive dependence in multivariate distributions, Comm. Statist. A Theory Methods, 10, 1183-1196 (1981) · Zbl 0471.62045 [2] Bingham, N. H.; Goldie, C. M.; Teugels, J. L., Regular Variation (1987), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0617.26001 [3] Block, H. W.; Savits, T. H.; Shaked, M., Some concepts of negative dependence, Ann. Probab., 10, 765-772 (1982) · Zbl 0501.62037 [4] Cline, D.B.H., Hsing, T., 1991. Large deviation probabilities for sums and maxima of random variables with heavy or subexponential tails. Preprint, A&M University, Texas.; Cline, D.B.H., Hsing, T., 1991. Large deviation probabilities for sums and maxima of random variables with heavy or subexponential tails. Preprint, A&M University, Texas. [5] Cline, D. B.H.; Samorodnitsky, G., Subexponentiality of the product of independent random variables, Stochastic Process. Appl., 49, 1, 75-98 (1994) · Zbl 0799.60015 [6] Ebrahimi, N.; Ghosh, M., Multivariate negative dependence, Comm. Statist. A Theory Methods, 10, 307-337 (1981) · Zbl 0506.62034 [7] Jelenković, P. R.; Lazar, A. A., Asymptotic results for multiplexing subexponential on-off processes, Adv. Appl. Probab., 31, 394-421 (1999) · Zbl 0952.60098 [8] Joag-Dev, K.; Proschan, F., Negative association of random variables with applications, Ann. Statist., 11, 286-295 (1983) · Zbl 0508.62041 [9] Klüppelberg, C.; Mikosch, T., Large deviations of heavy-tailed random sums with applications in insurance and finance, Adv. Appl. Probab., 34, 293-308 (1997) · Zbl 0903.60021 [10] Ng, K. W.; Tang, Q.; Yan, J.; Yang, H., Precise large deviations for sums of random variables with consistently varying tails, J. Appl. Probab., 41, 93-107 (2004) · Zbl 1051.60032 [11] Tang, Q., Insensitivity to negative dependence of the asymptotic behavior of precise large deviations, Electron. J. Probab., 11, 107-120 (2006) · Zbl 1109.60021 [12] Tang, Q.; Tsitsashvili, G., Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks, Stochastic Process. Appl., 108, 299-325 (2003) · Zbl 1075.91563 [13] Tang, Q. H.; Su, C.; Jiang, T.; Zhang, J. S., Large deviations for heavy-tailed random sums in compound renewal model, Probab. Statist. Lett., 52, 1, 91-100 (2001) · Zbl 0977.60034 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.