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Forgetting the initial distribution for Hidden Markov Models

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  • Douc, R.
  • Fort, G.
  • Moulines, E.
  • Priouret, P.

Abstract

The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions, and a convergence in expectation are considered. The results are illustrated using different HMM of interest: the dynamic tobit model, the nonlinear state space model and the stochastic volatility model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:4:p:1235-1256
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    References listed on IDEAS

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    2. 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.
    3. 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.
    4. 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..
    5. Emna Ghorbel & Mahdi Louati, 2024. "An expectation maximization algorithm for the hidden markov models with multiparameter student-t observations," Computational Statistics, Springer, vol. 39(6), pages 3287-3301, September.
    6. 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.
    7. Whiteley, Nick, 2021. "Dimension-free Wasserstein contraction of nonlinear filters," Stochastic Processes and their Applications, Elsevier, vol. 135(C), pages 31-50.

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