Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices

Abstract

This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite d × d-matrices. In particular, for conservative and subcritical affine processes on this cone we show that a finite log-moment of the stateindependent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: firstly, in a specific metric induced by the Laplace transform and secondly, in the Wasserstein distance under a first moment assumption imposed on the state-independent jump measure and an additional condition on the diffusion parameter.