  Affine jump-diffusions constitute a large class of continuous-time stochastic
models that are particularly popular in finance and economics due to their
analytical tractability. Methods for parameter estimation for such processes
require ergodicity in order establish consistency and asymptotic normality of
the associated estimators. In this paper, we develop stochastic stability
conditions for affine jump-diffusions, thereby providing the needed
large-sample theoretical support for estimating such processes. We establish
ergodicity for such models by imposing a `strong mean reversion' condition and
a mild condition on the distribution of the jumps, i.e. the finiteness of a
logarithmic moment. Exponential ergodicity holds if the jumps have a finite
moment of a positive order. In addition, we prove strong laws of large numbers
and functional central limit theorems for additive functionals for this class
of models.
