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Convergence of Empirical Processes for Interacting Particle Systems with Applications to Nonlinear Filtering

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  • P. Del Moral
  • M. Ledoux

Abstract

In this paper, we investigate the convergence of empirical processes for a class of interacting particle numerical schemes arising in biology, genetic algorithms and advanced signal processing. The Glivenko–Cantelli and Donsker theorems presented in this work extend the corresponding statements in the classical theory and apply to a class of genetic type particle numerical schemes of the nonlinear filtering equation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:1:d:10.1023_a:1007743111861
    DOI: 10.1023/A:1007743111861
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    References listed on IDEAS

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    1. 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.
    2. 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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