Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T18:51:49.683Z Has data issue: false hasContentIssue false
  • English
  • Français

First-passage-time moments of Markov processes

Published online by Cambridge University Press:  14 July 2016

David D. Yao
David D. Yao*
Affiliation:
Columbia University
*
∗ Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the first-passage times of continuous-time Markov chains. Based on the approach of generalized inverse, moments of all orders are derived and expressed in simple, explicit forms in terms of the ‘fundamental matrix'. The formulas are new and are also efficient for computation.

Keywords

GENERALIZED INVERSEFUNDAMENTAL MATRIXMATRIX ANALYSIS
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 939 - 945
Copyright
Copyright © Applied Probability Trust 1985 

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

[1] George, A. and Liu, J. W. (1981) Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
[2] Hunter, J. J. (1969) On the moments of Markov renewal processes. Adv. Appl. Prob. 1, 188–210.Google Scholar
[3] Hunter, J. J. (1982) Generalized inverses and their application to applied probability problems. Linear Algebra Appl. 45, 157–198.Google Scholar
[4] Keilson, J. (1979) Markov Chain Models: Rarity and Exponentiality. Springer-Verlag, New York.Google Scholar
[5] Kemeny, I. G. and Snell, J. L. (1976) Finite Markov Chains. Springer-Verlag, New York.Google Scholar