Jump to ContentJump to Main Navigation
Hidden Markov ProcessesTheory and Applications to Biology$
Users without a subscription are not able to see the full content.

M. Vidyasagar

Print publication date: 2014

Print ISBN-13: 9780691133157

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691133157.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 02 July 2022

Hidden Markov Processes: The Complete Realization Problem

Hidden Markov Processes: The Complete Realization Problem

(p.177) Chapter Seven Hidden Markov Processes: The Complete Realization Problem
Hidden Markov Processes

M. Vidyasagar

Princeton University Press

This chapter considers hidden Markov processes (HMPs), focusing on the so-called complete realization problem. It is quite easy to prove a universal necessary condition for the given process to have a hidden Markov model (HMM). However, this condition is not sufficient in general. In principle, one can derive a “necessary and sufficient condition,” but the “necessary and sufficient condition” is virtually a restatement of the problem to be solved and does not shed any insight into the solution. The chapter first introduces a very useful matrix known as the “Hankel” matrix before discussing the nonsufficiency of the finite Hankel rank condition, an abstract necessary and sufficient condition, and the existence of regular quasi-realizations. It also describes the spectral properties of alpha-mixing processes and goes on to analyze ultra-mixing processes and a sufficient condition for the existence of HMMs.

Keywords:   hidden Markov processes, complete realization problem, hidden Markov model, Hankel matrix, Hankel rank condition, quasi-realization, alpha-mixing process, ultra-mixing process

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.