Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-11T11:34:24.211Z Has data issue: false hasContentIssue false

Noisy fluctuating clocks for Markov chains

Published online by Cambridge University Press:  24 October 2008

J. E. Kennedy
Affiliation:
Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB

Abstract

In this paper we concern ourselves with the Q-matrices of time-substituted Markov chains where the time-substitutions are based on fluctuating clocks with noise. The results of this paper follow on naturally from the analysis in Kennedy and Williams [3], in which the problems of characterization and of calculation of these Q-matrices were addressed. Here, we study the Q-matrices as functions of the variance σ2 of the noise.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 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.)

References

REFERENCES

[1]Barlow, M. T., Rogers, L. C. G. and Williams, D.. Wiener–Hopf factorization for matrices. Séminaire de Probabilités XIV 784 (1980), 324331.CrossRefGoogle Scholar
[2]Kato, T.. A Short Introduction to Perturbation Theory for Linear Operators (Springer-Verlag, 1982).CrossRefGoogle Scholar
[3]Kennedy, J. E. and Williams, D.. Probabilistic factorization of a quadratic matrix polynomial. Math. Proc. Cambridge Philos. Soc. 107 (1990), 591600.CrossRefGoogle Scholar
[4]London, R. R., McKean, H. P., Rogers, L. C. G. and Williams, D.. A martingale approach to some Wiener-Hopf problems, II. Séminaire de Probabilités XVI 920 (1982), 6890.CrossRefGoogle Scholar
[5]Williams, D.. A ‘potential-theoretic’ note on the quadratic Wiener–Hopf equation for matrices. Séminaire de Probabilités XVI 920 (1982), 9094.Google Scholar