  We describe several different regimes which are possible in inflationary
cosmology. The simplest one is inflation without self-reproduction of the
universe. In this scenario the universe is not stationary. The second regime,
which exists in a broad class of inflationary models, is eternal inflation with
the self-reproduction of inflationary domains. In this regime local properties
of domains with a given density and given values of fields do not depend on the
time when these domains were produced. The probability distribution to find a
domain with given properties in a self-reproducing universe may or may not be
stationary, depending on the choice of an inflationary model. We give examples
of models where each of these possibilities can be realized, and discuss some
implications of our results for quantum cosmology. In particular, we propose a
new mechanism which may help solving the cosmological constant problem.
