  Gravitational waves from a variety of sources are predicted to superpose to
create a stochastic background. This background is expected to contain unique
information from throughout the history of the universe that is unavailable
through standard electromagnetic observations, making its study of fundamental
importance to understanding the evolution of the universe. We carry out a
search for the stochastic background with the latest data from LIGO and Virgo.
Consistent with predictions from most stochastic gravitational-wave background
models, the data display no evidence of a stochastic gravitational-wave signal.
Assuming a gravitational-wave spectrum of
Omega_GW(f)=Omega_alpha*(f/f_ref)^alpha, we place 95% confidence level upper
limits on the energy density of the background in each of four frequency bands
spanning 41.5-1726 Hz. In the frequency band of 41.5-169.25 Hz for a spectral
index of alpha=0, we constrain the energy density of the stochastic background
to be Omega_GW(f)<5.6x10^-6. For the 600-1000 Hz band, Omega_GW(f)<0.14*(f/900
Hz)^3, a factor of 2.5 lower than the best previously reported upper limits. We
find Omega_GW(f)<1.8x10^-4 using a spectral index of zero for 170-600 Hz and
Omega_GW(f)<1.0*(f/1300 Hz)^3 for 1000-1726 Hz, bands in which no previous
direct limits have been placed. The limits in these four bands are the lowest
direct measurements to date on the stochastic background. We discuss the
implications of these results in light of the recent claim by the BICEP2
experiment of the possible evidence for inflationary gravitational waves.
