Fractional Cox–Ingersoll–Ross process with small Hurst indices

Abstract

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 Y-epsilon, satisfying the SDE of the form dY(epsilon)(t) = (k/Y-epsilon(t)1({Y epsilon(t)>0})+epsilon -aY(epsilon)(t))dt + sigma dB(H) (t), as epsilon down arrow 0. Properties of such limit process are considered. SDE for both the limit process and the fractional Cox-Ingersoll-Ross process are obtained.