王开永,杨洋,袁锦泉.带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质[J].数学研究及应用,2023,43(3):335~349
带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质
The Uniform Asymptotics for the Tail of Poisson Shot Noise Process with Dependent and Heavy-Tailed Shocks
投稿时间:2022-05-16  修订日期:2022-08-22
DOI:10.3770/j.issn:2095-2651.2023.03.008
中文关键词:  Poisson噪音过程  相依冲击  重尾分布  一致渐近性质
英文关键词:Poisson shot noise process  dependent shock  heavy-tailed distribution  uniform asymptotics
基金项目:国家社会科学基金(Grant No.22BTJ060), 教育部人文社科基金(Grant No.20YJA910006),江苏省自然科学基金项目(Grant No.BK20201396),江苏省高校自然科学基金项目(Grant No.19KJA180003),中国香港特别行政区研究资助局资助项目(Grant No.HKU17306220),江苏省333高层次人才项目.
作者单位
王开永 苏州科技大学数学科学学院, 江苏 苏州 215009 
杨洋 南京审计大学统计与数据科学学院, 江苏 南京 211815 
袁锦泉 香港大学统计与精算学系, 薄扶林道, 香港 
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中文摘要:
      本文考虑了带有某种相依重尾冲击的Poisson噪音过程尾的一致渐近性质.当冲击是二元上尾渐近独立的非负随机变量具有长尾和控制变化尾分布且噪音函数具有正的上下界时,得到了过程尾概率的一致渐近公式.进而,当冲击具有连续的一致变化尾分布时,去除了噪音函数具有正的下界的限制.对于噪音函数不一定具有正的上界的情形,当冲击具有两两负象限相依结构时,也得到了一致渐近性结果.
英文摘要:
      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.
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