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We investigate the Stochastic Gravitational Wave Background (SGWB) producedby merging binary black holes (BBHs) and binary neutron stars (BNSs) in thefrequency ranges of LIGO/Virgo/Kagra and LISA. We develop three analyticalmodels, that are calibrated to the measured local merger rates, and complementthem with three population synthesis models based on the COSMIC code. Wediscuss the uncertainties, focusing on the impact of the BBH mass distribution,the effect of the metallicity of the progenitor stars and the time delaydistribution between star formation and compact binary merger. We also explorethe effect of uncertainties in binary stellar evolution on the background. ForBBHs, our analytical models predict $\Omega_{GW}$ in the range$[4.10^{-10}-1.10^{-9}]$ (25 Hz) and $[1.10^{-12}-4.10^{-12}]$ (3 mHz), andbetween $[2.10^{-10}-2.10^{-9}]$ (25 Hz) and $[7.10^{-13}- 7.10^{-12}]$ (3 mHz)for our population synthesis models. This background is unlikely to be detectedduring the LIGO/Virgo/Kagra O4 run, but could be detectable with LISA. Wepredict about 10 BBH and no BNS mergers that could be individually detectableby LISA for a period of observation of 4 years. Our study provides new insightsinto the population of compact binaries and the main sources of uncertainty inthe astrophysical SGWB.

Astrophysical Uncertainties in the Gravitational-Wave Background from Stellar-Mass Compact Binary Mergers