  Cosmological gamma-ray bursts may be powered by rotating black holes with
contemporaneous emission of gravitational radiation from a surrounding torus.
We calculate the resulting stochastic background radiation assuming strong
cosmological evolution and a uniform black hole mass distribution of M=
(4--14)M_odot. The predicted spectral flux density corresponds to a peak
spectral closure density of (1--2) times 10^{-7}, and has comparable
contributions at 450 Hz times kappa and over 300--450 Hz times kappa from
nearby and distant sources, respectively, where kappa refers to an uncertainty
factor of order unity in the radius of the torus. For two optimized advanced
LIGO-type detectors the proposed gravitational wave background could be
detectable within a year of integration.
