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On a Problem of Fluctuations of Sums of Independent Random Variables

Published online by Cambridge University Press:  05 September 2017

Lajos Takács
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Abstract

The author determines the distribution and the limit distribution of the number of partial sums greater than k (k = 0, 1, 2, …) for n mutually independent and identically distributed discrete random variables taking on the integers 1, 0, − 1, − 2, ….

Type
Part II — Probability Theory
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 29 - 37
Copyright
Copyright © 1975 Applied Probability Trust 

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References

[1] Andersen, E. S. (1949) On the number of positive sums of random variables. Skand. Aktuarietidskr. 32, 27–36.Google Scholar
[2] Andersen, E. S. (1953) On sums of symmetrically dependent random variables. Skand. Aktuarietidskr. 36, 123–138.Google Scholar
[3] Andersen, E. S. (1954) On the fluctuations of sums of random variables, II. Math. Scand. 2, 195–223.Google Scholar
[4] Erdös, P. and Kac, M. (1947) On the number of positive sums of independent random variables. Bull. Amer. Math. Soc. 53, 1011–1020.Google Scholar
[5] Heyde, C. C. (1967) Some local limit results in fluctuation theory. J. Austral. Math. Soc. 7, 455–464.Google Scholar
[6] Levy, P. (1939) Sur certains processus stochastiques homogènes. Compositio Math. 7, 283–339.Google Scholar
[7] Spitzer, F. (1956) A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc. 82, 323–339.Google Scholar
[8] Takács, L. (1961) The probability law of the busy period for two types of queuing processes. Operat. Res. 9, 402–407.CrossRefGoogle Scholar
[9] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. John Wiley, New York.Google Scholar