  The astrophysical stochastic gravitational wave background (SGWB) is mostly
produced from unresolved stellar binary mergers, and the number of events at
any moment of time is expected to be Poisson-distributed. The event rate is
governed by several astrophysical processes. The Poisson nature leads to
variation in the number of sources and this causes temporal variations in the
SGWB. The intrinsic temporal fluctuations of the SGWB are a rich source of
astrophysical information that can be explored via ongoing and future
gravitational wave experiments to classify the sources of the SGWB signal.
Along with several other methods to estimate the GW event rates from individual
sources, the study of the temporal variations of the SGWB signal provides an
independent method for estimating the event rates of the GW sources that
contribute to the SGWB. Along with direct estimates of event rates, this
approach can also distinguish between different sources contributing to the
SGWB signal and will be a useful probe of its evolution over a vast cosmic
volume. On averaging over observation times, the SGWB will be statistically
invariant under time translation. Statistical time translation symmetry of the
SGWB is expected due to the negligible evolution of the relevant cosmological
and astrophysical phenomena over the observation time-scales over which the
data is collected.
