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Future missions of gravitational-wave astronomy will be operated by space-based interferometers, covering very wide range of frequency band. Search for stochastic gravitational-wave backgrounds (GWBs) is one of the main target for such missions, and we here discuss the prospects for direct measurement of isotropic and anisotropic components of (primordial) GWBs around the frequency 0. 1-10 Hz. After extending the theoretical basis for correlation analysis, we evaluate the sensitivity and the signal-to-noise ratio for the proposed future missions of space interferometers, like Big-Bang Observer (BBO), Deci-Hertz Interferometer Gravitational-wave Observer (DECIGO) and recently proposed Fabry-Perot type DECIGO. The astrophysical foregrounds which are expected at the low frequency may be a big obstacle and significantly reduce the signal-to-noise ratio of GWBs. As a result, minimum detectable amplitude may reach h² \ = 10^-15 - 10^-16, as long as foreground point sources are properly subtracted. Based on the correlation analysis, we also discuss measurement of anisotropies of GWBs. As an example, sensitivity level required for detecting the dipole moment of GWB induced by the proper motion of our local system is closely examined.
Kudoh et al. (Mon,) studied this question.