Intersection local times of fractional Brownian motions with $H\in (0,1)$ as generalized white noise functionals

In ${\mathbb{R}}^d$, for any dimension $d\ge 1$, expansions of self-intersection local times of fractional Brownian motions with arbitrary Hurst coefficients in $(0,1)$ are presented. The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals.