In this paper, we establish a new connection between Cox–Ingersoll–Ross (CIR) and reflected Ornstein–Uhlenbeck (ROU) models driven by either a standard Wiener process or a fractional Brownian motion with $H>\frac{1}{2}$. We prove that, with probability 1, the square root of the CIR process converges uniformly on compacts to the ROU process as the mean reversion parameter tends to either ${\sigma }^2/4$ (in the standard case) or to 0 (in the fractional case). This also allows to obtain a new representation of the reflection function of the ROU as the limit of integral functionals of the CIR processes. The results of the paper are illustrated by simulations.

在本文中，我们在 Cox-Ingersoll-Ross (CIR) 和由标准维纳过程或分数布朗运动驱动的反射 Ornstein-Uhlenbeck (ROU) 模型之间建立了新的联系$H>\frac{\mathrm{1个}}{\mathrm{2个}}$. 我们证明，在概率为 1 的情况下，CIR 过程的平方根一致收敛于 ROU 过程的契约，因为均值回归参数趋向于${\sigma }^{\mathrm{2个}}/\mathrm{4个}$（在标准情况下）或为 0（在小数情况下）。这也允许获得 ROU 反射函数的新表示作为 CIR 过程的积分泛函的限制。本文的结果通过模拟进行了说明。