Existence of limiting distribution for affine processes

Abstract

In this paper, sufficient conditions are given for the existence of limiting distribution of a conservative affine process on the canonical state space ${\mathbb{R}}_{⩾0}^m\times {\mathbb{R}}^n$, where $m,n\in {\mathbb{Z}}_{⩾0}$ with $m+n>0$. Our main theorem extends and unifies some known results for OU-type processes on ${\mathbb{R}}^n$ and one-dimensional CBI processes (with state space ${\mathbb{R}}_{⩾0}$). To prove our result, we combine analytical and probabilistic techniques; in particular, the stability theory for ODEs plays an important role.

27 papes