Ergodic and strong Feller properties of affine processes

TL;DR

This paper establishes ergodic, exponential ergodic, and strong Feller properties for general (1+1)-affine Markov processes, using coupling methods and stochastic equations driven by time-space noises.

Contribution

It extends ergodic and strong Feller property results to a broad class of affine Markov processes with novel coupling techniques.

Findings

Proves ergodicity and exponential ergodicity in total variation for (1+1)-affine processes.

Establishes the strong Feller property for these processes.

Uses coupling methods based on stochastic equations driven by time-space noises.

Abstract

For general (1+1)-affine Markov processes, we prove the ergodicity and exponential ergodicity in total variation distances. Our methods follow the arguments of ergodic properties for L\'{e}vy-driven OU-processes and a coupling of CBI-processes constructed by stochastic equations driven by time-space noises. Then the strong Feller property is considered.