IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v124y2014i12p4149-4170.html
   My bibliography  Save this article

Exponential bounds for convergence of entropy rate approximations in hidden Markov models satisfying a path-mergeability condition

Author

Listed:
  • Travers, Nicholas F.

Abstract

A hidden Markov model (HMM) is said to have path-mergeable states if for any two states i,j there exist a word w and state k such that it is possible to transition from both i and j to k while emitting w. We show that for a finite HMM with path-mergeable states the block estimates of the entropy rate converge exponentially fast. We also show that the path-mergeability property is asymptotically typical in the space of HMM topologies and easily testable.

Suggested Citation

  • Travers, Nicholas F., 2014. "Exponential bounds for convergence of entropy rate approximations in hidden Markov models satisfying a path-mergeability condition," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4149-4170.
  • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:4149-4170
    DOI: 10.1016/j.spa.2014.07.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914001677
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2014.07.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Douc, R. & Fort, G. & Moulines, E. & Priouret, P., 2009. "Forgetting the initial distribution for Hidden Markov Models," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1235-1256, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Laruelle Sophie & Pagès Gilles, 2012. "Stochastic approximation with averaging innovation applied to Finance," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 1-51, January.
    2. Whiteley, Nick, 2021. "Dimension-free Wasserstein contraction of nonlinear filters," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 31-50.
    3. Jacob, Pierre E., 2012. "Contributions computationnelles à la statistique Bayésienne," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/12804 edited by Robert, Christian P..
    4. Nick Whiteley & Nikolas Kantas, 2017. "Calculating Principal Eigen-Functions of Non-Negative Integral Kernels: Particle Approximations and Applications," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1007-1034, November.
    5. van Handel, Ramon, 2009. "Uniform time average consistency of Monte Carlo particle filters," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3835-3861, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:4149-4170. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.