The Uniform Asymptotics for the Tail of Poisson Shot Noise Process with Dependent and Heavy-Tailed Shocks  

作　　者：Kaiyong WANG Yang YANG Kam Chuen YUEN 

机构地区：[1]School of Mathematical Sciences,Suzhou University of Science and Technology,Jiangsu 215009,P.R.China [2]School of Statistics and Data Science,Nanjing Audit University,Jiangsu 211815,P.R.China [3]Department of Statistics and Actuarial Science,The University of Hong Kong,Hong Kong,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第3期335-349,共15页数学研究及应用（英文版）

基　　金：Supported by the National Social Science Fund of China (Grant No.22BTJ060);the Humanities and Social Sciences Foundation of the Ministry of Education of China (Grant No.20YJA910006);the Natural Science Foundation of Jiangsu Province (Grant No.BK20201396);the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No.19KJA180003);the Grant from the Research Grants Council of the Hong Kong Special Administrative Region,China (Grant No.HKU17306220);the 333 High Level Talent Training Project of Jiangsu Province。

摘　　要：This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random variables with long-tailed and dominatedly varying tailed distributions, and the shot noise function has both positive lower and upper bounds, a uniform asymptotic formula for the tail probability of the process has been established.Furthermore, when the shocks have continuous and consistently varying tailed distributions, the positive lower-bound condition on the shot noise function can be removed. For the case that the shot noise function is not necessarily upper-bounded, a uniform asymptotic result is also obtained when the shocks follow a pairwise negatively quadrant dependence structure.

关 键 词：Poisson shot noise process dependent shock heavy-tailed distribution uniform asymptotics 

分 类 号：O211.6[理学—概率论与数理统计]