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The joint probability density function of the occupation time of a three-state problem

Published online by Cambridge University Press:  14 July 2016

Wei Shen Hsia
Wei Shen Hsia*
Affiliation:
University of Alabama
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Abstract

The joint probability density function of the occupation time of a three-state stochastic process with constant transition matrix: aij ≠ 0, i ≠ j, i, j = 1, 2, 3 but αii = 0, i = 1, 2, 3 is studied.

Keywords

STOCHASTIC PROCESSOCCUPATION TIMEPROBABILITY DENSITY FUNCTIONRANDOM WALK
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 57 - 64
Copyright
Copyright © Applied Probability Trust 1976 

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References

Gibson, A. E. and Conolly, B. W. (1971) On a three-state sojourn time problem. J. Appl. Prob. 8, 716–723.CrossRefGoogle Scholar
Good, I. J. (1961) The frequency count of a Markov chain and the transition to continuous time. Ann. Math. Statist. 32, 41–48.CrossRefGoogle Scholar
Parzen, E. (1960) Modern Probability Theory and its Applications. Wiley, New York.CrossRefGoogle Scholar