  The analysis of how a stochastic background of gravitational radiation
interacts with a spherical detector is given in detail, which leads to explicit
expressions for the system response functions, as well as for the
cross-correlation matrix of different readout channels. It is shown that
distinctive features of GW induced random detector excitations, relative to
locally generated noise, are in practice insufficient to separate the signal
from the noise by means of a single sphere, if prior knowledge on the GW
spectral density is nil. The situation significantly improves when such
previous knowledge is available, due to the omnidirectionality and multimode
capacities of a spherical GW antenna.
