IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v78y1998i1p69-95.html
   My bibliography  Save this article

Large deviations for interacting particle systems: Applications to non-linear filtering

Author

Listed:
  • Moral, P. Del
  • Guionnet, A.

Abstract

The non-linear filtering problem consists in computing the conditional distributions of a Markov signal process given its noisy observations. The dynamical structure of such distributions can be modelled by a measure valued dynamical Markov process. Several random particle approximations were recently suggested to approximate recursively in time the so-called non-linear filtering equations. We present an interacting particle system approach and we develop large deviations principles for the empirical measures of the particle systems. We end this paper extending the results to an interacting particle system approach which includes branchings.

Suggested Citation

  • Moral, P. Del & Guionnet, A., 1998. "Large deviations for interacting particle systems: Applications to non-linear filtering," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 69-95, October.
    • Handle: RePEc:eee:spapps:v:78:y:1998:i:1:p:69-95
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(98)00057-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Kunita, Hiroshi, 1971. "Asymptotic behavior of the nonlinear filtering errors of Markov processes," Journal of Multivariate Analysis, Elsevier, vol. 1(4), pages 365-393, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Naud, Cédric & Makowski, David & Jeuffroy, Marie-Hélène, 2007. "Application of an interacting particle filter to improve nitrogen nutrition index predictions for winter wheat," Ecological Modelling, Elsevier, vol. 207(2), pages 251-263.
    2. Jie Xiong & Yong Zeng, 2011. "A branching particle approximation to a filtering micromovement model of asset price," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 111-140, May.
    3. P. Del Moral & M. Ledoux, 2000. "Convergence of Empirical Processes for Interacting Particle Systems with Applications to Nonlinear Filtering," Journal of Theoretical Probability, Springer, vol. 13(1), pages 225-257, January.
    4. 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.

    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. Ying Jiao, 2009. "Multiple defaults and contagion risks," Working Papers hal-00441500, HAL.
    2. Budhiraja, A., 2001. "Ergodic properties of the nonlinear filter," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 1-24, September.
    3. Ying Jiao, 2009. "Multiple defaults and contagion risks," Papers 0912.3132, arXiv.org.
    4. Beatris Adriana Escobedo-Trujillo & Javier Garrido-Meléndez & Gerardo Alcalá & J. D. Revuelta-Acosta, 2022. "Optimal Control with Partially Observed Regime Switching: Discounted and Average Payoffs," Mathematics, MDPI, vol. 10(12), pages 1-28, June.
    5. LeGland, François & Oudjane, Nadia, 2003. "A robustification approach to stability and to uniform particle approximation of nonlinear filters: the example of pseudo-mixing signals," Stochastic Processes and their Applications, Elsevier, vol. 106(2), pages 279-316, August.
    6. Budhiraja, A. & Ocone, D., 1999. "Exponential stability in discrete-time filtering for non-ergodic signals," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 245-257, August.
    7. Deck, T., 2006. "Asymptotic properties of Bayes estimators for Gaussian Itô-processes with noisy observations," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 563-573, February.
    8. P. Del Moral & M. Ledoux, 2000. "Convergence of Empirical Processes for Interacting Particle Systems with Applications to Nonlinear Filtering," Journal of Theoretical Probability, Springer, vol. 13(1), pages 225-257, January.
    9. Papavasiliou, Anastasia, 2006. "Parameter estimation and asymptotic stability in stochastic filtering," Stochastic Processes and their Applications, Elsevier, vol. 116(7), pages 1048-1065, July.

    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:78:y:1998:i:1:p:69-95. 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.