  We apply adiabatic theorems developed for quantum mechanics to stochastic
annealing processes described by the classical master equation with a
time-dependent generator. When the instantaneous stationary state is unique and
the minimum decay rate g is nonzero, the time-evolved state is basically
relaxed to the instantaneous stationary state. By formulating an asymptotic
expansion rigorously, we derive conditions for the annealing time T that the
state is close to the instantaneous stationary state. Depending on the time
dependence of the generator, typical conditions are written as T> const/g^a
with 1<a<2. We also find that a rigorous treatment gives the scaling T>const|ln
g|/g^2.
