On almost sure noncentral limit theorems

LetX(t) be a fractional Brownian motion or Hermite process of indexH. SetX_m(t)=m^–HX(mt), which we view as an element ofC[0, 1]. Let {x} denote a point mass at x. ThenThe corresponding results for certain partial sums in the domain of attraction toX(t) are shown to hold.