Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-22T08:56:01.109Z Has data issue: false hasContentIssue false
  • English
  • Français

Occupation times for two state Markov chains

Published online by Cambridge University Press:  14 July 2016

P. J. Pedler
P. J. Pedler*
Affiliation:
Flinders University of South Australia
Get access Rights & Permissions [Opens in a new window]

Extract

Consider first a Markov chain with two ergodic states E1 and E2, and discrete time parameter set {0, 1, 2, ···, n}. Define the random variables Z0, Z1, Z2, ···, Znby then the conditional probabilities for k = 1,2,···, n, are independent of k. Thus the matrix of transition probabilities is

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971 , pp. 381 - 390
Copyright
Copyright © Applied Probability Trust 1971 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bromwich, T. J. I'a. (1926) An Introduction to the Theory of Infinite Series. 2nd Edition, Macmillan, London.Google Scholar
Darroch, J. N. and Morris, K. W. (1967) Some passage-time generating functions for discrete-time and continuous-time finite Markov chains. J. Appl. Prob. 4, 496–507.CrossRefGoogle Scholar
Darroch, J. N. and Morris, K. W. (1968) Passage-time generating functions for continuous-time finite Markov chains. J. Appl. Prob. 5, 414–426.CrossRefGoogle Scholar
Gabriel, K. R. (1959) The distribution of the number of successes in a sequence of dependent trials. Biometrika 46, 454–460.CrossRefGoogle Scholar