  We consider curved space quantum corrections to the equations of motion of
the inflaton field in the early Universe. Using the stochastic formalism in
phase space, we demonstrate that the quantum corrected evolution of the
inflaton can differ dramatically from its classical evolution when the mass
scales in the potential become large, which is naturally the case in
fundamental theories describing Planck scale physics. Using the example of the
cosine potential, we show that the prolonged, perhaps even eternal,
quantum--inflationary period is expected with a significant probability. This
feature of Planck scale potentials can be dangerous, but it offers also a
possibility of creating the inflationary phase in string or supergravity
models, where no natural realization of inflation has been found so far.
