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应用数学学报  1985, Vol. 8 Issue (2): 204-209    DOI:
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独立和分布为连续的充要条件
马志明, 安万福
中国科学院应用数学研究所
A SUFFICIENT AND NECESSARY CONDITION FOR A DISTRIBUTION OF INDEPENDENT SUM TO BE CONTINUOUS AND ITS APPLICATION TO TIME SERIES
Ma Zhi-ming, An Wan-fu
Institute ot Applied Mathematics, Academia Sinica
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摘要 1935年,Jessen和Wi-ntner证明了,如果{Xi}的分布都是纯跳跃的,那么X的分布是纯粹的,即或者是纯跳跃的,或者是奇异的,或者是连续的.三者必居其一.
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马志明
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Abstract: Let {Xn}n≥1 be a sequence of independent random variables and Xn a.s. converge.
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收稿日期: 1983-04-05;
引用本文:   
马志明,安万福. 独立和分布为连续的充要条件[J]. 应用数学学报, 1985, 8(2): 204-209.
Ma Zhi-ming,An Wan-fu. A SUFFICIENT AND NECESSARY CONDITION FOR A DISTRIBUTION OF INDEPENDENT SUM TO BE CONTINUOUS AND ITS APPLICATION TO TIME SERIES[J]. Acta Mathematicae Applicatae Sinica, 1985, 8(2): 204-209.
 
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[3] Gross, S. and W. L. Steiger, Least absolute diviation estimates in Autorgression with infinite variance, J. Appl. Prob., 16(1979), 104-116.
[4] Jessen, B. and Wintnet, A., Distribnfion Functions and the Riemann Zeta Function, Trans. Amer.Math. Soc., 38(1935), 48-88.
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[6] Stout,W.F., Almost Sure Convergence, Academic Press.New York, 1974, 97-99.
[7] Gaver, D.P. and Lewis, P. A., Filstorder Autoregressive Game Sequences and Point Processes,Adv. Appl. Prob., 12 (1980), 727-745.
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