Cumulative analysis of the association between the data of the gravitational wave detectors NAUTILUS and EXPLORER and the gamma ray bursts detected by BATSE and BeppoSAX

The statistical association between the output of the Gravitational Wave (GW) detectors EXPLORER and NAUTILUS and a list of Gamma Ray Bursts (GRBs) detected by the satellite experiments BATSE and BeppoSAX has been analyzed using cumulative algorithms. GW detector data collected between 1991 and 1999 have been searched for an energy excess in a 10 s interval around the GRB flux peak times. The cumulative analysis of the data relative to a large number of GRBs (387) allows to push the upper bound for the corresponding GW burst amplitude down to $h=2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$.