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Journal of Theoretical Probability

, Volume 13, Issue 1, pp 225–257 | Cite as

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

  • P. Del Moral
  • M. Ledoux
Article

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.

empirical processes Interacting particle systems Glivenko–Cantelli and Donsker theorems 

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© Plenum Publishing Corporation 2000

Authors and Affiliations

  • P. Del Moral
  • M. Ledoux

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