论文标题
关于仿射工艺的大型行为
On the large-time behaviour of affine Volterra processes
论文作者
论文摘要
我们显示了一类仿射类型多维随机伏尔泰系统的固定度量的存在。这些过程通常不是马尔可夫人，这是一个缺点，阻碍了他们的大量分析。我们通过将系统提升到Cuchiero和Teichmann引入的测量值随机PDE来避免此问题，从而我们检索了Markov属性。利用相关的广义伐木特性，我们将Krylov-Bogoliubov定理扩展到了无限维度设置，从而建立了一种不变措施的方法。我们提出了具体示例，包括数学金融的粗糙赫斯顿模型。
We show the existence of a stationary measure for a class of multidimensional stochastic Volterra systems of affine type. These processes are in general not Markovian, a shortcoming which hinders their large-time analysis. We circumvent this issue by lifting the system to a measure-valued stochastic PDE introduced by Cuchiero and Teichmann, whence we retrieve the Markov property. Leveraging on the associated generalised Feller property, we extend the Krylov-Bogoliubov theorem to this infinite-dimensional setting and thus establish an approach to the existence of invariant measures. We present concrete examples, including the rough Heston model from Mathematical Finance.
