The Uniform Asymptotics for the Tail of Poisson Shot Noise Process with Dependent and Heavy-Tailed Shocks
Received:May 16, 2022  Revised:August 22, 2022
Key Words: Poisson shot noise process   dependent shock   heavy-tailed distribution   uniform asymptotics  
Fund Project: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) and the 333 High Level Talent Training Project of Jiangsu Province.
Author NameAffiliation
Kaiyong WANG School of Mathematical Sciences, Suzhou University of Science and Technology, Jiangsu 215009, P. R. China 
Yang YANG School of Statistics and Data Science, Nanjing Audit University, Jiangsu 211815, P. R. China 
Kam Chuen YUEN Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, P. R. China 
Hits: 236
Download times: 233
Abstract:
      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.
Citation:
DOI:10.3770/j.issn:2095-2651.2023.03.008
View Full Text  View/Add Comment