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宽象限相依随机变量最大和与随机和的渐近尾概率
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Abstract:
本文研究了服从重尾分布的宽象限相依随机变量的最大和与随机和的渐近尾概率，其中随机变量服从长尾分布与控制变化尾分布族的交。结果显示在一定条件下，我们将已有的结果较好的推广到了宽象限相依结构，其最大和与随机和的渐近尾概率仍然成立。
In this paper, we consider the asymptotic tail probabilities of maxima of sums and random of sums for widely orthant dependent random variables with heavy tails. The random variables belong to the intersection of the long-tailed distributions class and the dominated varying tails distributions class. Under certain conditions, we will extend the results to the widely dependence structure, and the asymptotic tail probabilities of maxima of sums and random of sums are still true.
| [1] | Wang, D. and Tang, Q. (2004) Maxima of Sums and Random Sums for Negatively Associated Random Variables with Heavy Tailed. Statistics & Probability Letters, 68, 287-295. https://doi.org/10.1016/j.spl.2004.03.011 |
| [2] | Tang, Q. (2008) Insensitivity to Negative Dependence of Asymptotic Tail Probabilities of Sums and Maxima of Sums. Stochastic Analysis and Applications, 26, 435-450. https://doi.org/10.1080/07362990802006964 |
| [3] | Chen, Y. and Yuen, K. (2009) Sums of Pairwise Quasi-Asymptotically Independent Random Variables with Consistent Variation. Stochastic Models, 25, 76-89. https://doi.org/10.1080/15326340802641006 |
| [4] | Yang, Y., Wang, K., Remigijus, L. and ？i-aulys, J. (2011) Tail Behavior of Sums and Maxima of Sums of Dependent Subexponential Random Variables. Acta Ap-plicandae Mathematicae, 114, 219-231.
https://doi.org/10.1007/s10440-011-9610-1 |
| [5] | Yang, Y., Ignatavi？iūt？, E. and Siaulys, J. (2015) Conditional Tail Expectation of Randomly Weighted Sums with Heavy-Tailed Distributions. Statistics & Probability Letters, 105, 20-28. https://doi.org/10.1016/j.spl.2015.05.016 |
| [6] | Chen, Y. and Yang,Y. (2019) Bivariate Regular Variation among Randomly Weighted Sums in General Insurance. European Actuarial Journal, 9, 301-322. https://doi.org/10.1007/s13385-019-00197-y |
| [7] | Wang, K., Wang, Y. and Gao, Q. (2013) Uniform Asymptotics for the Finite-Time Ruin Probability of a New Dependent Risk Model with A Constant Interest Rate. Methodology and Computing in Applied Probability, 15, 109-124.
https://doi.org/10.1007/s11009-011-9226-y |
| [8] | Ghosh, M. (1981) Multivariate Negative Dependence. Communi-cations in Statistics—Theory and Methods, 10, 307-337. https://doi.org/10.1080/03610928108828041 |
| [9] | Block, H.W., Savits, T.H. and Shaked, M. (1982) Some Concepts of Negative Dependence. Annals of Probability, 10, 765-772. https://doi.org/10.1214/aop/1176993784 |
| [10] | Liu, L. (2009) Precise large Deviations for Dependent Random Var-iables with Heavy Tails. Statistics & Probability Letters, 79, 1290-1298. https://doi.org/10.1016/j.spl.2009.02.001 |
| [11] | Chen, Y., Chen, A. and Ng, K.W. (2010) The Strong Law of Large Numbers for Extend Negatively Dependent Random Variables. Journal of Applied Probability, 47, 908-922. https://doi.org/10.1239/jap/1294170508 |
| [12] | Liu, L. (2010) Necessary and Sufficient Conditions for Moderate De-viations of Dependent Random Variables with Heavy Tails. Science China Mathemaics A, 53, 1421-1434. https://doi.org/10.1007/s11425-010-4012-9 |
| [13] | Chen, Y., Wang, Y. and Wang, K. (2013) Asymptotic Results for Ruin Probability of a Two-Dimensional Renewal Risk Model. Stochastic Analysis and Applications, 31, 80-91. https://doi.org/10.1080/07362994.2013.741386 |
| [14] | Yang, Y. and Wang, Y. (2013) Tail Behavior of the Product of Two Dependent Random Variables with Applications to Risk Theory. Extremes, 16, 55-74. https://doi.org/10.1007/s10687-012-0153-2 |
| [15] | Chistyakov, V.P. (1964) A Theorem on Sums of Independent Positive Random Variables and Its Applications to Branching Process. Theory of Probability and Its Applications, 9, 640-648. https://doi.org/10.1137/1109088 |
| [16] | Cline, D.B.H. and Samorodnitsky, G. (1994) Subexponentiality of the Product of Independent Random Variables. Stochastic Processes and their Applications, 49, 75-98. https://doi.org/10.1016/0304-4149(94)90113-9 |
| [17] | Feller, W. (1969) One-Sided Analogues of Karamata’s Regu-lar Variation. L’Enseignement Mathématique, 15, 107-121. |
| [18] | Foss, S. and Zachary, S. (2003) The Maximum on a Random Time Interval of a Random Walk with Long-Tailed Increments and Negative Drift. Annals of Applied Probabil-ity, 13, 37-53. https://doi.org/10.1214/aoap/1042765662 |
| [19] | Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1987) Regular Variation. Cambridge University Press, Cambridge.
https://doi.org/10.1017/CBO9780511721434 |
| [20] | Tang, Q. and Tsitsiashvili, G. (2003) Precise Estimates for the Ruin Probability Infinite Horizon in a Discrete-Time Model with Heavy-Tailed Insurance and Financial Risks. Stochastic Processes and Their Applications, 108, 299-325.
https://doi.org/10.1016/j.spa.2003.07.001 |
