  In this paper we obtain regularity results for elliptic integro-differential
equations driven by the stronger effect of coercive gradient terms. This
feature allows us to construct suitable strict supersolutions from which we
conclude H\"older estimates for bounded subsolutions. In many interesting
situations, this gives way to a priori estimates for subsolutions. We apply
this regularity results to obtain the ergodic asymptotic behavior of the
associated evolution problem in the case of superlinear equations. One of the
surprising features in our proof is that it avoids the key ingredient which are
usually necessary to use the Strong Maximum Principle: linearization based on
the Lipschitz regularity of the solution of the ergodic problem. The proof
entirely relies on the H\"older regularity.
