A continuous stochastic background of gravitational waves (GWs) for burst s
ources is produced if the mean time interval between the occurrence of burs
ts is smaller than the average time duration of a single burst at the emiss
ion, i.e., the so-called duty cycle must be greater than one. To evaluate t
he background of GWs produced by an ensemble of sources, during their forma
tion, for trample, one needs to know the average energy flux emitted during
the formation of a single object and the formation rate of such objects as
well. In many cases the energy flux emitted during an event of production
of GWs is not known in detail; only characteristic values for the dimension
less amplitude and frequencies are known. Here we present a shortcut to cal
culate stochastic backgrounds of GWs produced from cosmological sources. Fo
r this approach it is not necessary to know in detail the energy flux emitt
ed at each frequency. Knowing the characteristic values for the "lumped" di
mensionless amplitude; and frequency we show that it is possible to calcula
te the stochastic background of GWs produced by an ensemble of sources.