论文标题
过渡密度的规律性和仿射跳转过程的终身性
Regularity of transition densities and ergodicity for affine jump-diffusion processes
论文作者
论文摘要
在本文中，我们研究了在规范状态空间上的仿射过程$ \ mathbb {r} _ {\ geq0}^{m} \ times \ times \ mathbb {r}^{n} $的过渡密度和指数性千差线。在扩散成分的Hörmander型条件下以及边界非处方假设下，我们得出了仿射过程的过渡密度的存在和规律性，然后证明了强的畸形特性。此外，我们还表明，在这些及其他亚临界条件下，规范状态空间上的相应仿射过程在总变化距离中成倍地呈颈。为了证明过渡密度的存在和规律性，我们得出了该过程特征函数的实际部分的一些精确估计。我们的成真结果是基于局部多布鲁蛋白条件加上过渡密度的规律性，适当应用Harris型定理的结果。
In this paper we study the transition density and exponential ergodicity in total variation for an affine process on the canonical state space $\mathbb{R}_{\geq0}^{m}\times\mathbb{R}^{n}$. Under a Hörmander-type condition for diffusion components as well as a boundary non-attainment assumption, we derive the existence and regularity of the transition density for the affine process and then prove the strong Feller property. Moreover, we also show that under these and the additional subcritical conditions the corresponding affine process on the canonical state space is exponentially ergodic in the total variation distance. To prove existence and regularity of the transition density we derive some precise estimates for the real part of the characteristic function of the process. Our ergodicity result is a consequence of a suitable application of a Harris-type theorem based on a local Dobrushin condition combined with the regularity of the transition densities.
