  We consider the error arising from the approximation of an N-particle
dynamics with its description in terms of a one-particle kinetic equation. We
estimate the distance between the j-marginal of the system and the factorized
state, obtained in a mean field limit as N $\rightarrow$ $\infty$. Our analysis
relies on the evolution equation for the "correlation error" rather than on the
usual BBGKY hierarchy. The rate of convergence is shown to be O(j 2 N) in any
bounded interval of time (size of chaos), as expected from heuristic arguments.
Our formalism applies to an abstract hierarchical mean field model with bounded
collision operator and a large class of initial data, covering (a) stochastic
jump processes converging to the homogeneous Boltzmann and the Povzner equation
and (b) quantum systems giving rise to the Hartree equation.
