Skip to main content Accessibility help
×
Home

Identifying Coefficients in the Spectral Representation for First Passage Time Distributions

  • Mark Brown (a1) and Yi-Shi Shao (a1)

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.

Copyright

References

Hide All
Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing, Holt, Rhinehart and Winston, New York, p. 9295.
Cinlar, E. (1975). Introduction to Stochastic Processes, Prentice Hall, Englewood Cliffs, New Jersey, p. 364381.
Cullen, C. G. (1967). Matrices and Linear Transformations, Addison-Wesley, Reading, Massachusetts, p. 72,145.
Gertsbakh, I. B. (1984). Asymptotic methods in reliablity theory: A review. Adv. Appl. Prob. 16: 147175.
Karlin, S. (1966). A First Course in Stochastic Processes, Academic Press, New York, p. 236484.
Keilson, J. (1979). Markov Chain Models-Rarity and Exponentiality, Springer-Verlag, New York, p. 3141, 5774.
Kemeny, J. G. and Snell, J. L. (1960). Finite Markov Chains, Van Nostrand, Princeton, New Jersey.
Ross, S. M. (1983). Stochastic Processes, John Wiley, New York, p. 143183.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed