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局部次指数分布的一类卷积封闭性的等价条件及应用

Equivalent Conditions for a Type of Convolution Closure of Local Subexponential Distributions and Applications
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摘要 给出了支撑在[0,∞)的局部次指数分布的一类卷积封闭性的若干等价条件,并在适当的条件下推广到了全空间.在此基础上,得到了对称化分布的局部渐近性的结果.上述结果可以蕴涵Embrechts和Goldie(1980)[1]及Geluk(2004)[2]非局部的相应结果,其中部分证明比[2]简单. This paper obtains some equivelent conditions for a type of convolution closure of local subexponential distributions on [0, ∞), which are also valid for distributions on (-∞,∞) under certain conditions. On the basis of these results, the local asymptotics for the distribution of symmetrization are given. The results above include the corresponding, non-local results of Embrechts and Goldie (1980)[1[ and Geluk (2004)[2]. Some of our proofs are more simple than those of Celuk (2004) .
出处 《应用概率统计》 CSCD 北大核心 2010年第5期469-476,共8页 Chinese Journal of Applied Probability and Statistics
基金 国家自然科学基金项目(10671139)资助
关键词 局部次指数分布 卷积封闭性 对称化 Local subexponential ditribution, convolution closure, symmetrization.
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参考文献7

  • 1Embrechts, P. and Goldie, .C., On closure and factorization properties of subexponebtial and related distributions. J. Austral. Math. Soc., 29(1980), 243-256.
  • 2Geluk, J.L., Asymptotics in the symmetrization inequality, Stat. Prob. Lett., 69(2004), 63-68.
  • 3Embrechts, P., Klfippelberg, C. and Mikosch, T., Modelling Extremal Events, Berlin, Springer, 1997.
  • 4Asmussen, S., Foss, S. and Korshunov, D., Asymptotics for sums of random variables with local subexponential behaviour, J. Theoret. Prob., 16(2003), 489-518.
  • 5Yuebao, W., Dongya, C. and Kaiyong, W., The closure of a local subexponential distribution with applications to the compound Poisson process, J. Appl. Prob., 42(2005), 1194-1203.
  • 6Yuebao, W., Yang, Y., Kaiyong, W. and Dongya, C., Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications, Insurance Mathematics and Economics, 40(2007), 256-266.
  • 7Leslie, J.R., On the non-closure under convolution of the subexponential distributions, J. Appl. Prob., 26(1989), 58-66.

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