  We present a detailed and systematic analysis of the coarse-grained,
nonequilibrium dynamics of a scalar inflaton field coupled to a fermion field
in the latter stages of the reheating period of inflationary cosmology. We
derive coupled nonperturbative equations for the inflaton mean field and
variance at two loops in a general curved spacetime, and show that the
equations of motion are real and causal, and that the gap equation for the
two-point function is dissipative due to fermion particle production. We then
specialize to the case of Minkowski space and small-amplitude inflaton
oscillations, and derive the perturbative one-loop dissipation and noise
kernels to fourth order in the Yukawa coupling constant; the normal-threshold
dissipation and noise kernels are shown to satisfy a zero-temperature
fluctuation-dissipation relation. We derive a Langevin equation for the
dynamics of the inflaton zero mode, and show that its variance is
non-negligible during reheating. Stochastic evolution of the inflaton may have
important astrophysical consequences.
