| 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. |
|
| Hits: 379 |
| Download times: 340 |
| 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 |
|
|
|
