If the effective cosmological constant is non-zero, our observable universe
may enter a stage of exponential expansion. In such case, regions of it may
tunnel back to the false vacuum of an inflaton scalar field, and inflation with
a high expansion rate may resume in those regions. An ``ideal'' eternal
observer would then witness an infinite succession of cycles from false vacuum
to true, and back. Within each cycle, the entire history of a hot universe
would be replayed. If there were several minima of the inflaton potential, our
ideal observer would visit each one of these minima with a frequency which
depends on the shape of the potential. We generalize the formalism of
stochastic inflation to analyze the global structure of the universe when this
`recycling' process is taken into account.Comment: 43 pages, 10 figure
