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.

arXiv comment27 papes

References in corpus (1)

• Stochastic differential equation with jumps for multi-type continuous state and continuous time branching processes with immigration

Cited by in corpus (4)

• Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes
• Long-time behavior for subcritical measure-valued branching processes with immigration
• On the anisotropic stable JCIR process
• Boundary behavior of multi-type continuous-state branching processes with immigration