  We study a two-state symmetric noise, with a given waiting time distribution
$\psi (\tau)$, and focus our attention on the connection between the four-time
and the two-time correlation functions. The transition of $\psi (\tau)$ from
the exponential to the non-exponential condition yields the breakdown of the
usual factorization condition of high-order correlation functions, as well as
the birth of aging effects. We discuss the subtle connections between these two
properties, and establish the condition that the Liouville-like approach has to
satisfy in order to produce a correct description of the resulting diffusion
process.
