On the Lack of Gaussian Tail for Rough Line Integrals along Fractional Brownian Paths

Horatio Boedihardjo, Xi Geng

We show that the tail probability of the rough line integral ${\int }_0^1\varphi (X_t)d{Y}_t$, where $(X,Y)$ is a 2D fractional Brownian motion with Hurst parameter $H\in (1/4,1/2)$ and…