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

In this paper the fractional Cox-Ingersoll-Ross process on ℝ₊ for H < 1/2 is defined as a square of a pointwise limit of the processes Yε, satisfying the SDE of the form dY_ε(t) = (^k _{Yε (t)1{Yε(t)>0}+ε} -aY_ε(t))dt +σdBH (t), as ε↓ 0. Properties of such limit process are considered. SDE for both the limit process and the fractional Cox-Ingersoll-Ross process are obtained. [ABSTRACT FROM AUTHOR]