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Strong lensing of gravitational waves is more likely for distant sources butpredicted event rates are highly uncertain with many astrophysical originsproposed. Here we open a new avenue to estimate the event rate of stronglylensed systems by exploring the amplitude of the stochastic gravitational wavebackground (SGWB). This method can provide a direct upper bound on the highredshift binary coalescing rates, which can be translated into an upper boundon the expected rate of strongly lensed systems. We show that from the ongoinganalysis of the Laser Interferometer Gravitational-wave Observatory(LIGO)-Virgo and in the future from the LIGO-Virgo design sensitivity stringentbounds on the lensing event rate can be imposed using the SGWB signal.Combining measurements of loud gravitational wave events with an unresolvedstochastic background detection will improve estimates of the numbers of lensedevents at high redshift. The proposed method is going to play a crucial inunderstanding the population of lensed and unlensed systems from gravitationalwave observations.

Inferring the lensing rate of LIGO-Virgo sources from the stochastic gravitational wave background