  We study the large deviations principle (LDP) for stationary solutions of a
class of stochastic differential equations (SDE) in infinite time intervals by
the weak convergence approach, and then establish the LDP for the invariant
measures of the SDE by the contraction principle. We further point out the
equivalence of the rate function of the LDP for invariant measures induced by
the LDP for stationary solutions and the rate function defined by
quasi-potential. This fact gives another view of the quasi-potential introduced
by Freidlin and Wentzell.
