Berry-Esséen bounds and almost sure CLT for the quadratic variation of the sub-bifractional Brownian motion

Abstract

Let $S^{H,K}=\{S^{H,K}(t),t\ge 0\}$ be the sub-bifractional Brownian motion(sbBm) of dimension 1, with indices $H\in (0,1)$ and $K\in (0,1].$ By using the Malliavin calculus and the Stein’s method, we mainly obtain Berry-Esséen bounds and prove the almost sure central limit theorem (ASCLT) for the quadratic variation of the sub-bifractional Brownian motion.

Keywords:

• Almost sure central limit theorem
• Berry-Esséen bounds
• Malliavin calculus
• quadratic variation
• sub-bifractional Brownian motion

Mathematics Subject Classification:

• 60G15
• 60G18
• 60F25

Acknowledgements

The authors thank Dr. Yong Chen for valued discussions.