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Finite-dimensional models for hidden Markov chains

Part of: Markov processes Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

Lakhdar Aggoun  and
Robert J. Elliott
Lakhdar Aggoun*
Affiliation:
University of Alberta
Robert J. Elliott*
Affiliation:
University of Alberta
*
* Postal address: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada.
* Postal address: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada.
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Abstract

A continuous-time, non-linear filtering problem is considered in which both signal and observation processes are Markov chains. New finite-dimensional filters and smoothers are obtained for the state of the signal, for the number of jumps from one state to another, for the occupation time in any state of the signal, and for joint occupation times of the two processes. These estimates are then used in the expectation maximization algorithm to improve the parameters in the model. Consequently, our filters and model are adaptive, or self-tuning.

Keywords

RECURSIVE FILTERUNNORMALIZED DENSITYREFERENCE PROBABILITYPARAMETER ESTIMATIONEM ALGORITHM

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 93E11: Filtering 60J35: Transition functions, generators and resolvents
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 146 - 160
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research partially supported by NSERC Grant A7964.

References

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