Asymptotics of the Cross-Variation of Young Integrals with Respect to a General Self-Similar Gaussian Process

Abstract

We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of order β ∈ (1/2, 3/4] is normal according to the values of β. We apply our results to two self-similar Gaussian processes: the subfractional Brownian motion and the bifractional Brownian motion.