Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T22:17:43.379Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Let X 1, X2, · ·· be a stationary sequence of random variables and E 1 , E 2 , · ··, EN mutually exclusive events defined on k consecutive X's such that the probabilities of the events have the sum unity. In the sequence E j1 , E j2 , · ·· generated by the X's, the mean waiting time from an event, say E j1 , 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

Information

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