  The quantum dynamics of correlated fermionic or bosonic many-body systems
following external excitation can be successfully studied using nonequilibrium
Green functions (NEGF) or reduced density matrix methods. Approximations are
introduced via a proper choice of the many-particle selfenergy or decoupling of
the BBGKY-hierarchy, respectively. These approximations are based on Feynman's
diagram approaches or on cluster expansions into single-particle and
correlation operators. In a recent paper [E. Schroedter, J.-P. Joost, and M.
Bonitz, Cond. Matt. Phys. \textbf{25}, 23401 (2022)] we have presented a
different approach where, instead of equations of motion for the many-particle
NEGF (or density operators), equations for the correlation functions of
fluctuations are analyzed. In particular, we derived the stochastic GW and
polarization approximations that are closely related to the nonequilibrium GW
approximation. Here, we extend this approach to the computation of two-time
observables depending on the specific ordering of the underlying operators. In
particular, we apply this extension to the calculation of the density
correlation function and dynamic structure factor of correlated Hubbard
clusters in and out of equilbrium.
