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Gravitational waves (GWs) are subject to gravitational lensing in the sameway as electromagnetic radiation. However, to date, no unequivocal observationof a lensed GW transient has been reported. Independently, GW observatoriescontinue to search for the stochastic GW signal which is produced by manytransient events at high redshift. We exploit a surprising connection betweenthe lensing of individual transients and limits to the background radiationproduced by the unresolved population of binary back hole mergers: we show thatit constrains the fraction of individually resolvable lensed binary black holesto less than $\sim 4\times 10^{-5}$ at present sensitivity. We clarify theinterpretation of existing, low redshift GW observations (obtained assuming nolensing) in terms of their apparent lensed redshifts and masses and exploreconstraints from GW observatories at future sensitivity. Based on our results,recent claims of observations of lensed events are statistically disfavoured.

Constraining the lensing of binary black holes from their stochastic background