  We study an idealized version of intermittent process leading the
fluctuations of a stochastic dichotomous variable $\xi$. It consists of an
overdamped and symmetric potential well with a cusp-like minimum. The
right-hand and left-hand portions of the potential corresponds to $\xi = W$ and
$\xi = -W$, respectively. When the particle reaches this minimum is injected
back to a different and randomly chosen position, still within the potential
well. We build up the corresponding Frobenius-Perron equation and we evaluate
the correlation function of the stochastic variable $\xi$, called
$\Phi_{\xi}(t)$. We assign to the potential well a form yielding $\Phi_{\xi}(t)
= (T/(t + T))^{\beta}$, with $\beta > 0$. We limit ourselves to considering
correlation functions with an even number of times, indicated for concision, by
$<12>$, $<1234>$ and, more, in general, by $<1 ... 2n>$. The adoption of a
treatment based on density yields $<1 ... 2n > = < 1 2 > ... < (2n-1) 2n>$. We
study the same dynamic problem using trajectories, and we establish that the
resulting two-time correlation function coincides with that afforded by the
density picture, as it should. We then study the four-times correlation
function and we prove that in the non-Poisson case it departs from the density
prescription, namely, from $<1234 > = < 12 > < 34>$. We conclude that this is
the main reason why the two pictures yield two different diffusion processes,
as noticed in an earlier work [M. Bologna, P. Grigolini, B.J. West, Chem. Phys.
{\bf 284}, (1-2) 115-128 (2002)].
