Limit theorems related to the integral functionals of one dimensional fractional Brownian motion

Abstract

In this paper, using the analog occupation time formulae associated with the integral functionals of one-dimensional fractional Brownian motion, we establish limit theorems for additive functionals ${\int }_0^{t}f(B_s^H)\mathit{ds}$ for suitable functions f, where $\{B_t^H,t\ge 0\}$ is a fractional Brownian motion.

Keywords:

• Limit theorems
• occupation time formulae
• fractional Brownian motion

Mathematics Subject Classification:

• 60F05
• 60G22

Additional information

Funding

The project was sponsored by NSFC (Nos. 11701589, 11671408, 11471340) and the Fundamental Research Funds for the Central Universities (No. 171gpy17).