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

@article{DelMoral2000ConvergenceOE,
  title={Convergence of Empirical Processes for Interacting Particle Systems with Applications to Nonlinear Filtering},
  author={Pierre Del Moral and Michel Ledoux},
  journal={Journal of Theoretical Probability},
  year={2000},
  volume={13},
  pages={225-257}
}
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. 
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