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