论文标题
Volterra Square-root过程：法律的平稳性和规律性
Volterra square-root process: Stationarity and regularity of the law
论文作者
论文摘要
$ \ mathbb {r} _+^m $上的Volterra Square-root过程是具有连续样本路径的仿射伏特拉过程。在与Volterra卷积内核相关的第二种解决方案上的合适可集成性条件下，我们确定了限制分布的存在。与经典的平方根扩散过程相反，这里的限制分布可能取决于该过程的初始状态。我们的结果表明，限制分布的非唯一性与Volterra卷积内核的整合性密切相关。使用指数 - 承包转换公式的扩展，我们还为与限制分布相关的固定过程构建。最后，我们证明时间边缘和限制分布仅限于状态空间的内部$ \ mathbb {r} _ {+}^m $，就Lebesgue量度而言，绝对是连续的。
The Volterra square-root process on $\mathbb{R}_+^m$ is an affine Volterra process with continuous sample paths. Under a suitable integrability condition on the resolvent of the second kind associated with the Volterra convolution kernel, we establish the existence of limiting distributions. In contrast to the classical square-root diffusion process, here the limiting distributions may depend on the initial state of the process. Our result shows that the non-uniqueness of limiting distributions is closely related to the integrability of the Volterra convolution kernel. Using an extension of the exponential-affine transformation formula we also give the construction of stationary processes associated with the limiting distributions. Finally, we prove that the time marginals as well as the limiting distributions, when restricted to the interior of the state space $\mathbb{R}_{+}^m$, are absolutely continuous with respect to the Lebesgue measure and their densities belong to some weighted Besov space of type $B_{1,\infty}^λ$.
