  We solve the impurity problem which arises within nonequilibrium dynamical
mean-field theory for the Hubbard model by means of a self-consistent
perturbation expansion around the atomic limit. While the lowest order, known
as the non-crossing approximation (NCA), is reliable only when the interaction
U is much larger than the bandwidth, low-order corrections to the NCA turn out
to be sufficient to reproduce numerically exact Monte Carlo results in a wide
parameter range that covers the insulating phase and the metal-insulator
crossover regime at not too low temperatures. As an application of the
perturbative strong-coupling impurity solver we investigate the response of the
double occupancy in the Mott insulating phase of the Hubbard model to a
dynamical change of the interaction or the hopping, a technique which has been
used as a probe of the Mott insulating state in ultracold fermionic gases.
