The problem of the optimal detection strategy to look for a stochastic g.w. background has been analyzed in many papers. For reviews on the subject refers to Refs.[10,11,12,13,14] and to the bibliography therein. The detection is based on the use of two or more detectors that should be properly oriented and ``near'', that is such that the correlation may contain the information on the stochastic background, but not too close, such that the local noises are uncorrelated. The analysis strategy is usually based on the cross-correlation function, that only depends on the common excitation of the detectors, as due to the gw stochastic background spectrum, and is not affected by the noises acting independently on the two detectors. The sensitivity to the stochastic signal improves with the observation time and with the bandwidth, as shown in all the cited papers.

The analysis of the Explorer and Nautilus detectors has been done, as described in [15], in the frequency domain using the Fourier Transforms of a Data Base.

Anyway, the problem of the optimal signal detection strategy is still open as many problems have to be studied and solved.

For example, the resonant detectors presently in operation show non stationary noise and also future detectors are expected to have non stationary noise. Another important point to be solved is the possibility of correlated noise in the outputs of the detectors. Joe Romano, in collaboration with B. Allen, J. Creighton, L. S. Finn, E. Flanagan and others, is studying the different statistics for this search and work is in progress in trying to solve the problems, as briefly described in the next session.