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Identifying Coefficients in the Spectral Representation for First Passage Time Distributions

Published online by Cambridge University Press:  27 July 2009

Mark Brown  and
Yi-Shi Shao
Mark Brown
Affiliation:
The City College City University of New York New York, New York
Yi-Shi Shao
Affiliation:
The City College City University of New York New York, New York
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Abstract

The spectral approach to first passage time distributions for Markov processes requires knowledge of the eigenvalues and eigenvectors of the infinitesimal generator matrix. We demonstrate that in many cases knowledge of the eigenvalues alone is sufficient to compute the first passage time distribution.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 1 , January 1987 , pp. 69 - 74
Copyright
Copyright © Cambridge University Press 1987

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References

Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing, Holt, Rhinehart and Winston, New York, p. 92–95.Google Scholar
Cinlar, E. (1975). Introduction to Stochastic Processes, Prentice Hall, Englewood Cliffs, New Jersey, p. 364–381.Google Scholar
Cullen, C. G. (1967). Matrices and Linear Transformations, Addison-Wesley, Reading, Massachusetts, p. 72,145.Google Scholar
Gertsbakh, I. B. (1984). Asymptotic methods in reliablity theory: A review. Adv. Appl. Prob. 16: 147–175.CrossRefGoogle Scholar
Karlin, S. (1966). A First Course in Stochastic Processes, Academic Press, New York, p. 236–484.Google Scholar
Keilson, J. (1979). Markov Chain Models-Rarity and Exponentiality, Springer-Verlag, New York, p. 31–41, 57–74.CrossRefGoogle Scholar
Kemeny, J. G. and Snell, J. L. (1960). Finite Markov Chains, Van Nostrand, Princeton, New Jersey.Google Scholar
Ross, S. M. (1983). Stochastic Processes, John Wiley, New York, p. 143–183.Google Scholar