  An integral relation between two functions parametrizing the bilocal field
strength correlator within the Stochastic Vacuum Model is obtained in the
effective Abelian-projected SU(2)-theory. This relation is independent of the
concrete properties of the ensemble of vortex loops, which are present in the
theory under study. By virtue of the lattice result stating that the infrared
asymptotic behaviours of these functions should have the same functional form,
the obtained relation enables one to find these behaviours, as well as the
infrared asymptotics of the bilocal correlator of densities of the vortex
loops. Those turn out to be exponentials, decreasing at the inverse mass of the
dual vector boson, times certain polynomials in the inverse integer powers of
the distance. This result agrees with the general predictions and the existing
lattice data better than the results of previous calculations, where these
powers were found to be half-integer ones.
