A limit theorem for occupation times of fractional Brownian motion

Recently, N. Kôno gave a limit theorem for occupation times of fractional Brownian motion, which result generalizes the well-known Kallianpur-Robbins law for two-dimensional Brownian motion. This paper studies a functional limit theorem for Kônoʹs result. It is proved that, under a suitable normalization, the limiting process is the inverse of an extremal process.