  We analyse the stochastic background of gravitational radiation emitted by a
cosmological population of core-collapse supernovae. The supernova rate as a
function of redshift is deduced from an observation-based determination of the
star formation rate density evolution. We then restrict our analysis to the
range of progenitor masses leading to black hole collapse. In this case, the
main features of the gravitational-wave emission spectra have been shown to be,
to some extent, independent of the initial conditions and of the equation of
state of the collapsing star, and to depend only on the black hole mass and
angular momentum. We calculate the overall signal produced by the ensemble of
black-hole collapses throughout the Universe, assuming a flat cosmology with
vanishing cosmological constant. Within a wide range of parameter values, we
find that the spectral strain amplitude has a maximum at a few hundred Hz with
an amplitude between $10^{-28}$ and $10^{-27} Hz^{-1/2}$; the corresponding
closure density, $\Omega_{GW}$, has a maximum amplitude ranging between
$10^{-11}$ and $10^{-10}$ in the frequency interval $\sim 1.5-2.5$ kHz.
Contrary to previous claims, our observation-based determination leads to a
duty cycle of order 0.01, making our stochastic backgound a non-continuous one.
Although the amplitude of our background is comparable to the sensitivity that
can be reached by a pair of advanced LIGO detectors, the characteristic
shot-noise structure of the predicted signal might be in principle exploited to
design specific detection strategies.
