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Forwards and backwards models for finite-state Markov processes

Published online by Cambridge University Press:  01 July 2016

B. D. O. Anderson  and
T. Kailath
B. D. O. Anderson*
Affiliation:
University of Newcastle, N.S.W.
T. Kailath*
Affiliation:
Stanford University
*
∗Postal address: Department of Electrical Engineering, University of Newcastle, Newcastle, N.S.W. 2308, Australia.
∗∗Postal address: Stanford University, Information Systems Laboratory, Stanford, CA 94305, U.S.A.
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Abstract

The construction and properties of reversible and dynamically reversible models for finite-state Markov processes are studied. Certain results on approximating processes with rational power spectra with dynamically reversible finite-state models are also obtained.

Keywords

REVERSIBLE PROCESSFINITE STATE PROCESSPOWER SPECTRAMARKOV PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 11 , Issue 1 , March 1979 , pp. 118 - 133
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

This work was supported by the U.S. Army Research Office, Grant DAAG29-77-C-0042, by the Australian Research Grants Committee, National Science Foundation under U.S.–Australian Cooperative Science Program, and by the Air Force Office of Scientific Research, Air Force Systems Command, under Contract AF44-620-74-C-0068.

References

1. Anderson, B. D. O. and Kailath, T. (1978) Forward, backward and dynamically reversible models for second order processes. In Proc. IEEE Internat. Symp. Circuits and Systems, IEEE, New York, 981–986.Google Scholar
2. Brockett, R. W. (1970) Finite Dimensional Linear Systems. Wiley, New York.Google Scholar
3. Brockett, R. W. (1977) Stationary covariance generation with finite state Markov processes. In Proc. 1977 Joint Auto. Control Conf., San Francisco, 1057–1060.Google Scholar
4. de Groot, S. R. (1966) Thermodynamics of Irreversible Processes. North-Holland, Amsterdam.Google Scholar
5. Guillemin, E. A. (1957) Synthesis of Passive Networks. Wiley, New York.Google Scholar
6. Keilson, J. (1965) A review of transient behaviour in regular diffusion and birth–death processes, II. J. Appl. Prob. 2, 405–428.Google Scholar
7. Keilson, J. (1971) On the structure of covariance functions and spectral density functions for processes reversible in time. Report CSS-71-03, University of Rochester.Google Scholar
8. Kolmogorov, A. N. (1936) Zur Theorie der Markoffschen Ketten. Math. Ann. 112, 155–160.Google Scholar
9. Lainiotis, D. G. (1976) General backwards Markov models. IEEE Trans. Auto. Control AC-21, 595–598.Google Scholar
10. Ljung, L. and Kailath, T. (1976) Backwards Markovian models for second-order stochastic processes. IEEE Trans. Inf. Theory IT-22, 488–491.Google Scholar
11. Sidhu, G. S. and Desai, U. B. (1976) New smoothing algorithms based on reversed-time lumped models. IEEE Trans. Auto Control AC-21, 538–541.Google Scholar
12. Whittle, P. (1975) Reversibility and acyclicity. In Perspectives in Probability and Statistics, ed. Gani, J., distributed by Academic Press, London, for the Applied Probability Trust, Sheffield, 217–224.Google Scholar