Fractional Cox–Ingersoll–Ross process with small Hurst indices
Volume 6, Issue 1 (2019), pp. 13–39
Pub. online: 21 December 2018
Type: Research Article
Open Access
Open Access
Received
27 August 2018
27 August 2018
Revised
3 December 2018
3 December 2018
Accepted
3 December 2018
3 December 2018
Published
21 December 2018
21 December 2018
Abstract
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.
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