Stochastic Background

A stochastic background of gravitational waves creates correlations between (otherwise) independent gravitational wave detector outputs. The correlation of the stochastic background of gravitational waves between two sites is 

To detect the stochastic background, one simply cross correlates the detector output at the two sites, with an appropriate weighting factor to suppress those frequencies at which the detector combination is not sensitive  

This method is tuned to detect a stochastic background of gravitational waves with an anticipated spectrum S2gw(/). 

If the stochastic background is significantly above the known instrumental noise, it is possible to measure it using the autocorrelation of the noise in a single detector rather than the cross correlation between detectors. The relevant detection method is the same as above but where hi(f) is the same as ft2(/X Si(f) is the same as S2(f), and y f) = 1. In this case, it makes sense to define the characteristic strain 

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Schmidt [16] thoroughly analyzed the problem of uncertainties in measuring the mean lifetime with a small number of detected nuclei, including the presence of a stochastic background. The crucial point was that the measurement was supposed to last until complete decay of the nuclide. The treatment was based on the maximum likelihood approach the 90 percent confidence intervals were tabulated. 

In the Table 1 we can see the result for the Olomouc region. In this case the network was adjusted in such a way that there is no dead-end link. It is apparent that there are no major differences among the results apart from the strategy a) which can be caused by the stochastic background of the algorithm. It can be seen that the disintegration of the network into a higher number of components need not represent the worst-case scenario. Moreover, in certain cases the best value of the loss function corresponds to several combinations of interrupted hnks. 

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