On the ergodicity of a three-factor CIR model

This study introduces the CIR3 model, a three-factor model characterized by stochastic and correlated trends and volatilities. The paper focuses on establishing the Wasserstein ergodicity of this model, a task not achievable through conventional means such as the Dobrushin theorem. Instead, alternative mathematical approaches are employed, including considerations of topological aspects of Wasserstein spaces and Kolmogorov equations for measures. Remarkably, the methodology developed here can also be applied to prove the Wasserstein ergodicity of the widely recognized three-factor Chen model.