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Noisy fluctuating clocks for Markov chains
Published online by Cambridge University Press: 24 October 2008
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
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 199 - 205
- Copyright
- Copyright © Cambridge Philosophical Society 1991
References
REFERENCES
[1]Barlow, M. T., Rogers, L. C. G. and Williams, D.. Wiener–Hopf factorization for matrices. Séminaire de Probabilités XIV 784 (1980), 324–331.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), 591–600.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), 68–90.CrossRefGoogle Scholar
[5]Williams, D.. A ‘potential-theoretic’ note on the quadratic Wiener–Hopf equation for matrices. Séminaire de Probabilités XVI 920 (1982), 90–94.Google Scholar