P. Del Moral et M. Ledoux, Convergence of empirical processes for interacting particle systems with applications to nonlinear filtering, J THEOR PR, 13(1), 2000, pp. 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 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.