They are not well-behaved. The main problem is that one cannot control the
radius of convergence when using perturbation techniques. Just outside the radius of
convergence, higher-order approximations can easily behave extremely badly, and even
within the radius of convergence one can expect higher- but .nite-order perturbation
solutions to display problematic oscillations. In contrast, with projection methods
one can control the radius of convergence. Pruning, the solution proposed to deal
with explosive behavior of higher-order perturbation solutions, is shown to be highly
distortionary. A simple alternative based on short samples and rejection sampling is
proposed and shown to be much less distortive.