Coupling methods and exponential ergodicity for two-factor affine processes

TL;DR

This paper proves exponential ergodicity for a broad class of two-factor affine processes using a universal coupling approach, applicable even with correlated noises and interactions.

Contribution

It introduces a universal coupling method to establish exponential ergodicity for general two-factor affine processes, including complex interactions and correlated noises.

Findings

Exponential ergodicity under $L^1$-Wasserstein distance is established.

The method applies to processes with general CIR components and interactions.

It extends to some models beyond traditional two-factor processes.

Abstract

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.