Another notion of stationarity - the same or different?

Hi Everybody!

My question may be very trivial, however, I am not able to answer it.

In standard time series theory we have two notions of stationarity:
strict sense (SSS) and wide sense stationarity (WSS). The series that
is SSS satisfies the equation

$$ L(X(t_1),\ldots,X(t_k)) = L(X(t_1+\tau),\ldots,X(t_k+\tau)) $$

for any $ t_1, \ldots,t_k $ and $ \tau $. Now define a new class of
time series (name them another sense of stationarity - ASS) as the
series that satisfy

$$ E X(t_1+\tau),\ldots,X(t_k+\tau)=E X(t_1),\ldots,X(t_k) $$

It is easy to see that $SSS \subset ASS \subset WSS$. Is ASS really
smaller (therefore different) than SSS class? Or rather ASS=SSS?

I would be very grateful for any clues.

.

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