The generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2

Litan Yan, Chao Chen, Junfeng Liu

Let $B^H$ be a fractional Brownian motion with Hurst index $0<H<1/2$. In this paper we study the {\it generalized quadratic covariation} $[f(B^H),B^H{]}^{(W)}$ defined by $$ [f(B^H),…