  In this paper, we discuss the warm inflation model with both a Langevin
equation and a generalized Langevin equation scenario. As a brief picture to
illustrate the basic properties of stochastic differential equation in warm
inflation, this paper is started from a simple condition with constant
dissipative coefficient. In this model, we prove the perturbed inflaton field
exhibits a stationary process on large scale, so the perturbed field has a
scale-invariant power spectrum. Then we study the warm inflation with a
generalized Langevin equation scenario. The perturbed field in such model also
shows a stationary process and the power spectrum is quite similar to the one
in cold inflation. If choosing an appropriate fluctuation-dissipation relation,
we can get a spectrum same as the cold inflation. In a word, we attempt to show
the rationality of warm inflationary scenario via statistical physics method.
