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On sums of random variables defined on a two-state Markov chain

Published online by Cambridge University Press:  14 July 2016

H. J. Helgert
H. J. Helgert*
Affiliation:
Cornell Aeronautical Laboratory, Inc., Buffalo
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Extract

Assume the sequence of random variables x0, x1, x2, ··· forms a two-state, homogeneous Markov chain with transition probabilities and initial probabilities

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 3 , December 1970 , pp. 761 - 765
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Kendall, M. G. (1958) The Advanced Theory of Statistics. Vol. 1. Hafner Publishing Company, New York.Google Scholar
[2] Volkov, I. S. (1958) On the distribution of sums of random variables defined on a homogeneous Markov chain with a finite number of states. Theor. Probability Appl. 3, 384–399.Google Scholar
[3] Gabriel, K. R. (1959) The distribution of the number of successes in a sequence of dependent trials. Biometrika 46, 454–460.Google Scholar
[4] Gnedenko, B. V. (1965) Lehrbuch der Wahrscheinlichkeitsrechnung. Akademie-Verlag Berlin.Google Scholar