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The measurement of gravitational waves produced by binary black-hole mergersat the Advanced LIGO has encouraged extensive studies on the stochasticgravitational wave background. Recent studies have focused on gravitationalwave sources made of the same species, such as mergers from binary primordialblack holes or those from binary astrophysical black holes. In this paper, westudy a new possibility -- the stochastic gravitational wave backgroundproduced by mergers of one primordial black hole and one astrophysical blackhole. Such systems are necessarily present if primordial black holes exist. Westudy the isotropic gravitational wave background produced through the historyof the Universe. We find it is very challenging to detect such a signal. Wealso demonstrate that it is improper to treat the gravitational waves producedby such binaries in the Milky Way as a directional stochastic background, dueto a very low binary formation rate.

Stochastic Gravitational Wave Background from PBH-ABH Mergers