Many fractional processes can be represented as an integral over a family of Ornstein–Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily high polynomial order. This explains the potential, but also some limitations of such representations as the basis of Monte Carlo schemes for fractional volatility models such as the rough Bergomi model.

中文翻译：

---

分数过程的马尔可夫表示的强收敛率

许多分数过程可以表示为 Ornstein-Uhlenbeck 过程族的积分。这种表示自然适用于数值离散化，在本文中显示出具有任意高多项式阶数的强收敛速度。这解释了这种表示的潜力，但也解释了作为分数波动率模型（如粗糙的 Bergomi 模型）的 Monte Carlo 方案的基础的一些限制。