  We compute the Wiener chaos decomposition of the signature for a class of
Gaussian processes, which contains fractional Brownian motion (fBm) with Hurst
parameter H in (1/4, 1). At level 0, our result yields an expression for the
expected signature of such processes, which determines their law [CL16]. In
particular, this formula simultaneously extends both the one for 1/2 < H-fBm
[BC07] and the one for Brownian motion (H = 1/2) [Faw03], to the general case H
> 1/4, thereby resolving an established open problem. Other processes studied
include continuous and centred Gaussian semimartingales.
