Convergence of empirical processes for interacting particle systems with applications to nonlinear filtering

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 Donsk er theorems presented in this work extend the corresponding statements in t he classical theory and apply to a class of genetic type particle numerical schemes of the nonlinear filtering equation.