  This work is devoted to the study of conservative affine processes on the
canonical state space $D = $R_+^m \times \R^n$, where $m + n > 0$. We show that
each affine process can be obtained as the pathwise unique strong solution to a
stochastic equation driven by Brownian motions and Poisson random measures.
Then we study the long-time behavior of affine processes, i.e., we show that
under first moment condition on the state-dependent and log-moment conditions
on the state-independent jump measures, respectively, each subcritical affine
process is exponentially ergodic in a suitably chosen Wasserstein distance.
Moments of affine processes are studied as well.
