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The analysis method currently proposed to search for isotropic stochasticradiation of primordial or astrophysical origin with the Laser InterferometerSpace Antenna (LISA) relies on the combined use of two LISA channels, one ofwhich is insensitive to gravitational waves, such as the symmetrised Sagnac.For this method to work, it is essential to know how the instrumental noisepower in the two channels are related to one another; however, no quantitativeestimates of this key information are available to date. The purpose of ourstudy is to assess the performance of the symmetrised Sagnac method fordifferent levels of prior information regarding the instrumental noise. Wedevelop a general approach in the framework of Bayesian inference and anend-to-end analysis algorithm based on Markov Chain Monte Carlo methods tocompute the posterior probability density functions of the relevant modelparameters. We apply this method to data released as part of the second roundof the Mock LISA Data Challenges. For the selected (and somewhat idealised)cases considered here, we find that a prior uncertainty of a factor ~2 in theratio between the power of the instrumental noise contributions in the twochannels allows for the detection of isotropic stochastic radiation. Moreimportantly, we provide a framework for more realistic studies of LISA'sperformance and development of analysis techniques in the context of searchesfor stochastic signals.

Search for a stochastic gravitational-wave signal in the second round of the Mock LISA Data Challenges