Cross-variation of Young integral with respect to long-memory fractional Brownian motions

Abstract

We study the asymptotic behaviour of the cross-variation of two-dimensional processes having the form of a Young integral with respect to a fractional Brownian motion of index $H \textgreater{} 1/ 2$. When $H$ is smaller than or equal to $3/4$, we show asymptotic mixed normality. When $H$ is strictly bigger than $3/4$, we obtain a limit that is expressed in terms of the difference of two independent Rosenblatt processes.

arXiv comment15 pages

References in corpus (2)

• Analysis of the Rosenblatt process
• Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins

Cited by in corpus (1)

• Forecasting of time data with using fractional Brownian motion