Hostname: page-component-74656f9884-c52kr Total loading time: 0 Render date: 2026-11-09T09:46:35.130Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral Analysis, without Eigenvectors, for Markov Chains

Published online by Cambridge University Press:  27 July 2009

Mark Brown
Mark Brown
Affiliation:
The City College, CUNY New York, New York 10031
Get access Rights & Permissions [Opens in a new window]

Abstract

The Lagrange-Sylvester interpolation polynomial approach provides a simple, eigenvector-free representation for finite diagonalizable matrices. This paper discusses the Lagrange-Sylvester methodology and applies it to skip free to the right Markov chains. It leads to relatively simple, eigenvalue-based expressions for first passage time distributions and transition probabilities.

Information

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 2 , April 1991 , pp. 131 - 144
Copyright
Copyright © Cambridge University Press 1991

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.)

Article purchase

Temporarily unavailable

References

Aldous, D. & Diaconis, P. (1987). Strong uniform times and finite random walks. Advances in Applied Mathematics, 8: 69–87.CrossRefGoogle Scholar
Birkoff, G. & MacLane, S. (1962). A Survey of Modern Algebra. New York: Macmillan.Google Scholar
Birkoff, G. & Rota, G. (1969). Ordinary differential equations, 2nd ed.Waltham, MA: Blaisdell.Google Scholar
Brown, M. (1990). Consequences of monotonicity for Markov transition functions. City College, CUNY Report No. MB89−03.CrossRefGoogle Scholar
Brown, M. & Shao, Y. (1987). Identifying coefficients in the spectral representation for first passage time distributions. Probability in the Engineering and Informational Sciences 1: 69–74.CrossRefGoogle Scholar
Cinlar, E. (1975). Introduction to stochastic processes. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Diaconis, P. & Fill, J.A. (1990). Strong stationary times via a new form of duality. The Annals of Probability, 18:1483–1522.CrossRefGoogle Scholar
Dunford, N. & Schwartz, J.T. (1958). Linear operators, Part I: General theory. New York: Interscience.Google Scholar
Gantmacher, F.R. (1959). The theory of matrices, Vol. I. New York: Chelsea House.Google Scholar
Karlin, S. (1966). A first course in stochastic processes. New York: Academic Press.Google Scholar
Keilson, J. (1979). Markov chain models-Rarity and exponentialily. New York: Springer-Verlag.CrossRefGoogle Scholar
Lang, S. (1966). Linear algebra. New York: Addison-Wesley.Google Scholar