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The mean waiting time to a repetition

Published online by Cambridge University Press:  01 July 2016

Gunnar Blom
Gunnar Blom*
Affiliation:
University of Lund
*
∗Postal address: Department of Mathematical Statistics, University of Lund, Box 725, S-220 07 Lund, Sweden.
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Abstract

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Let X1, X2, · ·· be a stationary sequence of random variables and E1, E2, · ··, EN mutually exclusive events defined on k consecutive X's such that the probabilities of the events have the sum unity. In the sequence Ej1, Ej2, · ·· generated by the X's, the mean waiting time from an event, say Ej1, to a repetition of that event is equal to N (under a mild condition of ergodicity). Applications are given.

Keywords

STATIONARITYBERNOULLI TRIALSMARKOV CHAINUPCROSSINGS AND DOWNCROSSINGS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 216 - 218
Copyright
Copyright © Applied Probability Trust 1983 

References

Breiman, L. (1968) Probability. Addison-Wesley, Reading, Mass.Google Scholar
Johnson, N. L. (1968) Repetitions. Amer. Math. Monthly 75, 382–383.CrossRefGoogle Scholar