  Astrometry, the precise measurement of star motions, offers an alternative
avenue to investigate low-frequency gravitational waves through the spatial
deflection of photons, complementing pulsar timing arrays reliant on timing
residuals. Upcoming data from Gaia and Roman can not only cross-check pulsar
timing array findings but also explore the uncharted frequency range bridging
pulsar timing arrays and LISA. We present an analytical framework to evaluate
the feasibility of detecting a gravitational wave background, considering
measurement noise and the intrinsic variability of the stochastic background.
Furthermore, we highlight astrometry's crucial role in uncovering key
properties of the gravitational wave background, such as spectral index and
chirality, employing information-matrix analysis. Finally, we simulate the
emergence of quadrupolar correlations, commonly referred to as the generalized
Hellings-Downs curves.
