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Extreme mass ratio inspirals (EMRIs) are among the primary targets for theLaser Interferometer Space Antenna (LISA). The extreme mass ratios of thesesystems result in relatively weak GW signals, that can be individually resolvedonly for cosmologically nearby sources (up to $z\approx2$). The incoherentpiling up of the signal emitted by unresolved EMRIs generate a confusion noise,that can be formally treated as a stochastic GW background (GWB). In thispaper, we estimate the level of this background considering a collection ofastrophysically motivated EMRI models, spanning the range of uncertaintiesaffecting EMRI formation. To this end, we employed the innovative AugmentedAnalytic Kludge waveforms and used the full LISA response function. For eachmodel, we compute the GWB SNR and the number of resolvable sources. Compared tosimplified computations of the EMRI signals from the literature, we find thatfor a given model the GWB SNR is lower by a factor of $\approx 2$ whereas thenumber of resolvable sources drops by a factor 3-to-5. Nonetheless, the vastmajority of the models result in potentially detectable GWB which can alsosignificantly contribute to the overall LISA noise budget in the 1-10 mHzfrequency range.

Computation of stochastic background from extreme mass ratio inspiral populations for LISA