Fractional Cox–Ingersoll–Ross process with small Hurst indices

Modern Stochastics: Theory and Applications

Yuliya Mishura¹  Anton Yurchenko-Tytarenko¹ 

[1] Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska St., 64/13, Kyiv 01601, Ukraine;

关键词: Fractional Cox–Ingersoll–Ross process;    fractional Brownian motion;    Stochastic differential equation;    pathwise Stratonovich integral;   

DOI  :  10.15559/18-VMSTA126

来源: DOAJ

【 摘 要 】

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 $d{Y_{\varepsilon }}(t)=(\frac{k}{{Y_{\varepsilon }}(t){1_{\{{Y_{\varepsilon }}(t)>0\}}}+\varepsilon }-a{Y_{\varepsilon }}(t))dt+\sigma d{B^{H}}(t)$, as $\varepsilon \downarrow 0$. Properties of such limit process are considered. SDE for both the limit process and the fractional Cox–Ingersoll–Ross process are obtained.

【 授权许可】

Unknown