Stationarity and ergodicity for an affine two factor model
Matyas Barczy, Leif Doering, Zenghu Li, Gyula Pap
TL;DR
This paper investigates the conditions under which a 2-dimensional affine process, involving an alpha-root process, admits a unique stationary distribution and exhibits ergodicity, with specific results for the case when alpha equals 2.
Contribution
It establishes the existence of a unique stationary distribution for the affine process when alpha is in (1,2], and proves ergodicity specifically for alpha=2.
Findings
Unique stationary distribution exists for alpha in (1,2]
Ergodicity is proven for alpha=2
Results contribute to understanding long-term behavior of affine processes
Abstract
We study the existence of a unique stationary distribution and ergodicity for a 2-dimensional affine process. The first coordinate is supposed to be a so-called alpha-root process with \alpha\in(1,2]. The existence of a unique stationary distribution for the affine process is proved in case of \alpha\in(1,2]; further, in case of \alpha=2, the ergodicity is also shown.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · advanced mathematical theories