Generation of fluctuations during inflation: comparison of stochastic
  and field-theoretic approaches
  We prove that the stochastic and standard field-theoretical approaches
produce exactly the same results for the amount of light massive scalar field
fluctuations generated during inflation in the leading order of the slow-roll
approximation. This is true both in the case for which this field is a test one
and inflation is driven by another field, and the case for which the field
plays the role of inflaton itself. In the latter case, in order to calculate
the average of the mean square of the gauge-invariant inflaton fluctuation, the
logarithm of the scale factor $a$ has to be used as the time variable in the
Fokker-Planck equation in the stochastic approach. The implications of particle
production during inflation for the second stage of inflation and for the
moduli problem are also discussed. The case of a massless self-interacting test
scalar field in a de Sitter background with a zero initial renormalized mean
square is also considered in order to show how the stochastic approach can
easily produce results corresponding to diagrams with an arbitrary number of
scalar field loops in the field-theoretical approach (explicit results up to 4
loops inclusive are presented).
