  We consider continuous time random walks (CTRW) and discuss situations
pertinent to aging. These correspond to the case when the initial state of the
system is known not at preparation (at $t=0$) but at the later instant of time
$t_1>0$ (intermediate-time initial condition). We derive the generalized aging
diffusion equation for this case and express it through a single memory kernel.
The results obtained are applied to the practically relevant case of the
equilibrated random walks. We moreover discuss some subtleties in the setup of
the aging subdiffusion problem and show that the behavior of the system depends
on what was taken as the intermediate-time initial condition: whether it was
coordinate of one particle given by measurement or the whole probability
distribution. The two setups lead to different predictions for the evolution of
a system. This fact stresses the necessity of a precise definition of aging
statistical ensembles.
