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We consider chaotic inflation in the theories with the effective potentialsphi^n and e^{\alpha\phi}. In such theories inflationary domains containingsufficiently large and homogeneous scalar field \phi permanently produce newinflationary domains of a similar type. We show that under certain conditionsthis process of the self-reproduction of the Universe can be described by astationary distribution of probability, which means that the fraction of thephysical volume of the Universe in a state with given properties (with givenvalues of fields, with a given density of matter, etc.) does not depend ontime, both at the stage of inflation and after it. This represents a strongdeviation of inflationary cosmology from the standard Big Bang paradigm. Wecompare our approach with other approaches to quantum cosmology, and illustratesome of the general conclusions mentioned above with the results of a computersimulation of stochastic processes in the inflationary Universe.

From the big bang theory to the theory of a stationary universe