Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model 被引量：1

Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model

下载PDF

导出

摘要 Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained. Consider a multidimensional renewal risk model, in which the claim sizes {X_k, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.

作者 SHEN Xin-mei FU Ke-ang ZHONG Xue-ting

机构地区 School of Mathematical Sciences School of Statistics and Mathematics

出处《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2018年第4期491-502,共12页 高校应用数学学报（英文版）（B辑）

基金 Supported by the National Natural Science Foundation of China(Nos.11571058&11301481) Humanities and Social Science Foundation of the Ministry of Education of China(No.17YJC910007) Zhejiang Provincial Natural Science Foundation of China(No.LY17A010004) Fundamental Research Funds for the Central Universities(No.DUT17LK31)

关键词 Precise large deviation SIZE-DEPENDENT Consistent variation Multidimensional risk model Renewal counting process Precise large deviation Size-dependent Consistent variation Multidimensional risk model Renewal counting process

分类号 O1 [理学—基础数学]

引文网络
相关文献

参考文献2

1Jinghai FENG,Panpan ZHAO,Libin JIAO.Local Precise Large Deviations for Independent Sums in Multi-Risk Model[J].Journal of Mathematical Research with Applications,2014,34(2):240-248. 被引量：2
2Xinmei SHEN,Yuqing NIU,Hailan TIAN.Precise large deviations for sums of random vectors with dependent components of consistently varying tails[J].Frontiers of Mathematics in China,2017,12(3):711-732. 被引量：1

二级参考文献12

1A. V. NAGAEV. Integral limit theorems with regard to large deviations when Cramer's condition is not satisfied (I). Teor. Verojatnost. i Primenen, 1969, 14: 51-63.
2A. V. NAGAEV. Integral limit theorems with regard to large deviations when Cramer's condition is not satisfied (II). Teor. Verojatnost. i Primenen, 1969, 14: 203-216.
3D. B. H. CLINE, G. SAMORODNITSKY. Subexponentiality of the product ofindependent random variables. Stochastic Process. Appl., 1994, 49(1): 75-98.
4K. W. NG, Qihe TANG, Jiaan YAN, et al.. Precise large deviations for sums of random variables with consistently varying tails. J. Appl. Probab., 2004, 41(1): 93-107.
5Qihe TANG. Insensitivity to negative dependence of the asymptotic behavior of precise large deviations. Electron. J. Probab., 2006, 11(4): 107-120.
6Shijie WANG, Wensheng WANG. Precise large deviations for sums of random variables with consistently varying tails in multi-risk models. J. Appl. Probab., 2007, 44(4): 889--900.
7Dawei LU. Lower and upper bounds of large deviation for sums of subexponential claims in a multi-risk model. Statist. Probab. Lett., 2011, 81(12): 1911-1919.
8Dawei LU. Lower bounds of large deviation for sums of long-tailed claims in a multi-risk model. Statist. Probab. Lett., 2012, 82(7): 1242-1250.
9R. A. DONEY. A large deviation local limit theorem. Math. Proc. Cambridge Philos. Soc., 1989, 105(3): 575-577.
10Yang YANG, R. LEIPUS, J. SIAULYS. Local precise large deviations for sums of random variables with O-regularly varying densities. Statist. Probab. Lett., 2010, 80(19-20): 1559-1567.