Coupling methods and exponential ergodicity for two-factor affine processes

In this paper, by invoking the coupling approach, we establish exponential ergodicity under the $L^1$-Wasserstein distance for two-factor affine processes. The method employed herein is universal in a certain sense so that it is applicable to general two-factor affine processes, which allow that the first component solves a general CIR process, and that there are interactions in the second component, as well as that the Brownian noises are correlated; and even to some models beyond two-factor processes.