  We study the generation of a stochastic gravitational wave (GW) background
produced from a population of core-collapse supernovae, which form black holes
in scenarios of structure formation. We obtain, for example, that the formation
of a population (Population III) of black holes, in cold dark matter scenarios,
could generate a stochastic GW background with a maximum amplitude of $h_{\rm
BG} \simeq 10^{-24}$ and corresponding closure energy density of
$\Omega_{\rm{GW}}\sim 10^{-7}$, in the frequency band $\nu_{\rm{obs}} \simeq
30-470 {\rm Hz}$ (assuming a maximum efficiency of generation of GWs, namely,
$\epsilon_{\rm GW_{\rm max}} = 7\times 10^{-4}$) for stars forming at redshifts
$z\simeq 30-10.$ We show that it will be possible in the future to detect this
isotropic GW background by correlating signals of a pair of `advanced' LIGO
observatories (LIGO III) at a signal-to-noise ratio of $\simeq 40$. We discuss
what astrophysical information could be obtained from a positive (or even a
negative) detection of such a GW background generated in scenarios such as
those studied here. One of them is the possibility of obtaining the initial and
final redshifts of the emission period from the observed spectrum of GWs.
