Fractional Cox--Ingersoll--Ross process with small Hurst indices

In this paper the fractional Cox-Ingersoll-Ross process on $\mathbb{R}_+$ for $H 0\}}+\varepsilon}-a Y_{\varepsilon}(t))dt+\sigma dB^H(t)$, as $\varepsilon\downarrow0$. Properties of such limit process are considered. SDE for both the limit process and the fractional Cox-Ingersoll-Ross process are obtained.