Regularity of transition densities and ergodicity for affine jump‐diffusions

Abstract

This paper studies the transition density and exponential ergodicity for affine processes on the canonical state space ℝ 𝑚 ≥0 × ℝ 𝑛 . Under a Hörmander-type condition for diffusion components as well as a boundary nonattainment condition, we derive the existence and regularity of the transition densities and then prove the strong Feller property of the associated semigroup. Moreover, we also show that, under an additional subcriticality condition on the drift, the corresponding affine process is exponentially ergodic in the total variation distance.