  We carry out a perturbative analysis, of high order in the tunneling
parameter, of the ground state of the homogeneous Bose-Hubbard model in the
Mott insulator phase. This is made possible by a diagrammatic process chain
approach, derived from Kato's representation of the many-body perturbation
series, which can be implemented numerically in a straightforward manner. We
compute ground-state energies, atom-atom correlation functions, density-density
correlations, and occupation number fluctuations, for one-, two-, and
three-dimensional lattices with arbitrary integer filling. A phenomenological
scaling behavior is found which renders the data almost independent of the
filling factor. In addition, the process chain approach is employed for
calculating the boundary between the Mott insulator phase and the superfluid
phase with high accuracy. We also consider systems with dimensionalities d>3,
thus monitoring the approach to the mean-field limit. The versatility of the
method suggests further applications to other systems which are less well
understood.
