  We propose a data processing technique that allows searches for a stochastic
background of gravitational radiation with data from a single detector. Our
technique exploits the difference between the coherence time of the
gravitational wave (GW) signal and that of the instrumental noise affecting the
measurements. By estimating the auto-correlation function of the data at an
off-set time that is longer than the coherence time of the noise {\underbar
{but}} shorter than the coherence time of the GW signal, we can effectively
enhance the power signal-to-noise ratio (SNR) by the square-root of the
integration time. The resulting SNR is comparable in magnitude to that
achievable by cross-correlating the data from two co-located and co-aligned
detectors whose noises are uncorrelated. Our method is general and it can be
applied to data from ground- and space-based detectors, as well as from pulsar
timing experiments.
