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

Acta Mathematicae Applicatae Sinica ›› 1985, Vol. 8 ›› Issue (2) : 204-209.

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Acta Mathematicae Applicatae Sinica ›› 1985, Vol. 8 ›› Issue (2) : 204-209. DOI: 10.12387/C1985023

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
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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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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. Acta Mathematicae Applicatae Sinica, 1985, 8(2): 204-209 https://doi.org/10.12387/C1985023

References

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[4] Jessen, B. and Wintnet, A., Distribnfion Functions and the Riemann Zeta Function, Trans. Amer.Math. Soc., 38(1935), 48-88.
[5] Breiman, L., Probability, Addison-Wesley, Reading, Massachaserts, 1968, 49-50.
[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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