Standard and fractional reflected Ornstein–Uhlenbeck processes as the limits of square roots of Cox–Ingersoll–Ross processes

Figures & data

Figure 1. Sample paths of $Y_{\epsilon }^H(t)$ (black) and $\frac{1}{2}{\int }_0^t\frac{\epsilon }{Y_{\epsilon }^H(s)}\mathrm{d}s$ (grey) for $\epsilon =0.0001$ and different Hurst indices H. (a) H = 0.6 (b) H = 0.7 (c) H = 0.8 (d) H = 0.9

Figure 2. Comparison of the $Y_{\epsilon }^H$ with $\epsilon =1$ , $\epsilon =0.5$ , $\epsilon =0.25$ $\epsilon =0.1$ , $\epsilon =0.0001$ (lines with colors ranging from light grey to dark grey) and the RFOU process (bold black line). Note that the purple path ($\epsilon =0.0001$) is not visible on the plot since it almost completely coincides with the bold black trajectory of the RFOU process.