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We present the analysis of between 50 and 100 hrs of coincidentinterferometric strain data used to search for and establish an upper limit ona stochastic background of gravitational radiation. These data come from thefirst LIGO science run, during which all three LIGO interferometers wereoperated over a 2-week period spanning August and September of 2002. The methodof cross-correlating the outputs of two interferometers is used for analysis.We describe in detail practical signal processing issues that arise whenworking with real data, and we establish an observational upper limit on af^{-3} power spectrum of gravitational waves. Our 90% confidence limit isOmega_0 h_{100}^2 < 23 in the frequency band 40 to 314 Hz, where h_{100} is theHubble constant in units of 100 km/sec/Mpc and Omega_0 is the gravitationalwave energy density per logarithmic frequency interval in units of the closuredensity. This limit is approximately 10^4 times better than the previous,broadband direct limit using interferometric detectors, and nearly 3 timesbetter than the best narrow-band bar detector limit. As LIGO and otherworldwide detectors improve in sensitivity and attain their design goals, theanalysis procedures described here should lead to stochastic backgroundsensitivity levels of astrophysical interest.Comment: 26 pages, 17 figure

Analysis of first LIGO science data for stochastic gravitational waves