  First, we establish an abstract ergodic result on $\mR^d$. Classical ergodic
results on $\mR^d$ require that the process is irreducible, we weaken it to
some weak form of irreducibility in this article. The main method used in this
article is coupling. Then, we apply our abstract ergodic result to stochastic
differential equations driven by a L\'evy noise and obtain a new result.
