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Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails 被引量：44

Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails
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摘要 This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances. This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.
作者 LIU Li School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China
出处 《Science China Mathematics》 SCIE 2010年第6期1421-1434,共14页 中国科学：数学（英文版）
基金 supported by National Natural Science Foundation of China(Grant No.10571139) the Research Foundation of Education Bureau of Hubei Province,China (Grant No.Q200710002)
关键词 MODERATE deviation extended negative dependence consistently VARYING TAIL random SUM moderate deviation extended negative dependence consistently varying tail random sum
分类号 O211.5 [理学—概率论与数理统计]
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  • 1Linnik, Yu. V.: Limit theorems allowing large deviations for the sums of independent variables Ⅰ, Ⅱ. Theory Probab. Appl., 6, 145-161,377-391 (1961).
  • 2Heyde, C. C.: A contribution to the theory of large deviations for sums of independent random variables. Z. Wahr., 7, 303-308 (1967).
  • 3Heyde, C. C.: On large deviation problems for sums of random variables which are not attracted to the normal law. Ann. Math. Statist., 38, 1575-1578 (1967).
  • 4Heyde, C. C.: On large deviation probabilities in the case of attraction to a nonnormal stable law. Sankyd., 30, 253-258 (1968).
  • 5Nagaev, A. V.: Integral limit theorems for large deviations when Cramer's condition is not fulfilled I, II. Theory Probab. Appl., 14, 51-64, 193-208 (1969).
  • 6Nagaev, A. V.: Limit theorems for large deviations when Cramer's conditions are violated. Izv. Akad. Nauk UzSSR Set. Fiz-Mat. Nauk., 7, 17-22 (1969).
  • 7Nagaev, S. V.: Large deviations for sums of independent random variables. In: Transactions of the Sixth Prague Conference on Information Theory, Random Processes and Statistical Decision Functions, 657-674 Academic, Prague, 1973.
  • 8Nagaev, S. V.: Large Deviations of sums of independent random variables. Ann. Probab., 7, 745-789 (1979).
  • 9Cline, D. B. H., Hsing, T.: Large deviation probabilities for sums of random variables with heavy or subexponential tails, Preprint, 1998, Texas A&M University.
  • 10Mikosch, T., Nagaev, A. V.: Large Deviations of Heavy-Tailed Sums with Applications in Insurance. Extremes, 1, 81-110 (1998).

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Science China Mathematics
2010年 第6期

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