论文标题
分数Cox- ingersoll-带有小赫斯特指数的摩擦过程
Fractional Cox--Ingersoll--Ross process with small Hurst indices
论文作者
论文摘要
在本文中，$ \ mathbb {r} _+$ for $ h <1/2 $上的分数cox-ingersoll-ross过程定义为$ y _ {\ y _ {\ varepsilon} $的点的平方，满足表格$ d y _ _ _ _ _ { y _ _ {\ varepsilon}（t）\ mathbb {1} _ {\ {y _ {\ _ {\ varepsilon}（t）（t）> 0 \}}}+\ varepsilon} -a y _ y _ y _ _ {\ varepsilon} $ \ varepsilon \ downarrow0 $。考虑了这种极限过程的属性。获得了限制过程和分数Cox-Intersoll-ross过程的SDE。
In this paper the fractional Cox-Ingersoll-Ross process on $\mathbb{R}_+$ for $H<1/2$ is defined as a square of a pointwise limit of the processes $Y_{\varepsilon}$, satisfying the SDE of the form $d Y_{\varepsilon}(t)=( \frac{k}{ Y_{\varepsilon}(t)\mathbb{1}_{\{ Y_{\varepsilon}(t)>0\}}+\varepsilon}-a Y_{\varepsilon}(t))dt+σdB^H(t)$, 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.
