  We present the analysis of between 50 and 100 hrs of coincident
interferometric strain data used to search for and establish an upper limit on
a stochastic background of gravitational radiation. These data come from the
first LIGO science run, during which all three LIGO interferometers were
operated over a 2-week period spanning August and September of 2002. The method
of cross-correlating the outputs of two interferometers is used for analysis.
We describe in detail practical signal processing issues that arise when
working with real data, and we establish an observational upper limit on a
f^{-3} power spectrum of gravitational waves. Our 90% confidence limit is
Omega_0 h_{100}^2 < 23 in the frequency band 40 to 314 Hz, where h_{100} is the
Hubble constant in units of 100 km/sec/Mpc and Omega_0 is the gravitational
wave energy density per logarithmic frequency interval in units of the closure
density. This limit is approximately 10^4 times better than the previous,
broadband direct limit using interferometric detectors, and nearly 3 times
better than the best narrow-band bar detector limit. As LIGO and other
worldwide detectors improve in sensitivity and attain their design goals, the
analysis procedures described here should lead to stochastic background
sensitivity levels of astrophysical interest.
