关于大偏差概率的一个界(英文)The bounds of large deviations probalilities
曹晓敏;高珊;
摘要(Abstract):
研究得到了关于随机和S(t)=∑N(t)i=1Xi,t≥0大偏差的幂的一个界,其中(N(t))t≥0是一族非负整值随机变量,(Xn)n∈N是独立同分布的随机变量,其共同的分布函数是F与(N(t))t≥0独立.本结论是在假设分布函数F的右尾属于ERV族的情况下得到的.
关键词(KeyWords): ERV族;大偏差
基金项目(Foundation): 国家自然科学基金资助项目(10471076)
作者(Authors): 曹晓敏;高珊;
参考文献(References):
- [1]Asmussen S,Claudia Klüppelberg.Large deviations results for subexponential tails with applicationsto insurance risk[J].Stochastic Processes and their Applications,1996,64∶103-125.
- [2]Mikosch T,Nagaev A V.Large deviations of heavy-tailed random sums with a applications ininsurance[J].Extremes,1998,1(1)∶81-110.
- [3]Klüppelberg C,Mikosch T.Large deviations of heavy-tailed random sums with applications ininsurance and finance[J].J.Appl.Prob.,1997,34∶293-308.
- [4]Su Chun,Tang Qihe,Jiang Tao.A contribution to large deviations for heavy-tailed random sums[J].Science in China,2001,44A(4)∶438-444.
- [5]Liu Yan,Hu Yijun.Large deviations for a heavy-tailed stationary sequence[J].J.of Math.,2003,23∶11-23.
- [6]Embrechts P,Klüpplberg C,Mikosch T.Modelling Extremal Events for Insurance and Finance[M].Berlin∶Springer-Verlag,1997.