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

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    4. 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.

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