A 2-D Realization Theory for Markov Chains

Jose A. Ramos; Erik I. Verriest

doi:10.1109/CDC.1990.203709

A 2-D Realization Theory for Markov Chains

Jose A. Ramos
, Erik I. Verriest

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we study the dynamics of time homogeneous Markov chain models from a state-space modeling point of view. It is shown that a Markov chain model can be embedded in a 2-D realization theory where markov parameters correspond to higher-order transition probabilities. The implications of formulating a Markov chain model in this state-space domain is that many equivalent representations may exist, some of which may have better robustness properties. A modified Hankel approximation algorithm is presented which exactly matches all the Markov parameters. The algorithm is an extension of the 2-D harmonic retrieval algorithm of D.V.B. Rao et al.

Original language	American English
Journal	Proceedings of the 29th Conference on Decision and Control
DOIs	https://doi.org/10.1109/CDC.1990.203709
State	Published - Dec 1 1990
Event	29th IEEE Conference on Decision and Control - Honolulu, United States Duration: Dec 5 1990 → Dec 7 1990 https://ieeexplore.ieee.org/xpl/conhome/164/proceeding

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Computer Sciences

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10.1109/CDC.1990.203709License: Unspecified

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abstract = " In this paper we study the dynamics of time homogeneous Markov chain models from a state-space modeling point of view. It is shown that a Markov chain model can be embedded in a 2-D realization theory where markov parameters correspond to higher-order transition probabilities. The implications of formulating a Markov chain model in this state-space domain is that many equivalent representations may exist, some of which may have better robustness properties. A modified Hankel approximation algorithm is presented which exactly matches all the Markov parameters. The algorithm is an extension of the 2-D harmonic retrieval algorithm of D.V.B. Rao et al.",

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AU - Verriest, Erik I.

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N2 - In this paper we study the dynamics of time homogeneous Markov chain models from a state-space modeling point of view. It is shown that a Markov chain model can be embedded in a 2-D realization theory where markov parameters correspond to higher-order transition probabilities. The implications of formulating a Markov chain model in this state-space domain is that many equivalent representations may exist, some of which may have better robustness properties. A modified Hankel approximation algorithm is presented which exactly matches all the Markov parameters. The algorithm is an extension of the 2-D harmonic retrieval algorithm of D.V.B. Rao et al.

AB - In this paper we study the dynamics of time homogeneous Markov chain models from a state-space modeling point of view. It is shown that a Markov chain model can be embedded in a 2-D realization theory where markov parameters correspond to higher-order transition probabilities. The implications of formulating a Markov chain model in this state-space domain is that many equivalent representations may exist, some of which may have better robustness properties. A modified Hankel approximation algorithm is presented which exactly matches all the Markov parameters. The algorithm is an extension of the 2-D harmonic retrieval algorithm of D.V.B. Rao et al.

UR - https://nsuworks.nova.edu/gscis_facarticles/383

U2 - 10.1109/CDC.1990.203709

DO - 10.1109/CDC.1990.203709

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JO - Proceedings of the 29th Conference on Decision and Control

JF - Proceedings of the 29th Conference on Decision and Control

T2 - 29th IEEE Conference on Decision and Control

Y2 - 5 December 1990 through 7 December 1990

ER -

A 2-D Realization Theory for Markov Chains

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